A data set is approximately normally distributed. Let x and y be scores from the data set where x has a z-score of 3 and y has a z-score of 2.
State the event that is less likely to occur:
Event 1: Randomly selecting a score in the data set greater than x.
Event 2: Randomly selecting a score in the data set greater than y.
State the event that is less likely to occur:
Event 3: Randomly selecting a score in the data set less than y.
Event 4: Randomly selecting a score in the data set less than x.
A data set is approximately normally distributed. Let x and y be scores from the data set where x has a z-score of 4.17 and y has a z-score of 4.73.
State the event that is more likely to occur:
Event 1: Randomly selecting a score in the data set greater than y.
Event 2: Randomly selecting a score in the data set greater than x.
State the event that is more likely to occur:
Event 3: Randomly selecting a score in the data set less than x.
Event 4: Randomly selecting a score in the data set less than y.
A data set is approximately normally distributed. Let x and y be scores from the data set where x has a z-score of -2 and y has a z-score of -3. Determine which of the following event is most likely to occur:
Randomly selecting a score in the data set less than x.
Randomly selecting a score in the data set less than y.
Randomly selecting a score in the data set greater than y.
Randomly selecting a score in the data set greater than x.
A data set is approximately normally distributed. Let x and y be scores from the data set where x has a z-score of 2 and y has a z-score of -1.
State the event that is more likely to occur:
Event 1: Randomly selecting a score in the data set that is less than y.
-
Event 2: Randomly selecting a score in the data set that is more than x.
State the event that is less likely to occur:
Event 3: Randomly selecting a score in the data set that is more than y.
-
Event 4: Randomly selecting a score in the data set that is less than x.
The heights of sunflowers at a nursery are approximately normally distributed with mean 159\text{ cm} and standard deviation 28\text{ cm}. The heights and their z-scores are given in the table:
| \text{Height (cm)} | 268.2 | 91.8 |
|---|---|---|
| z\text{-score} | 3.9 | -2.4 |
State the event that is more likely to occur:
Event 1: Randomly selecting a sunflower from the nursery that's taller than 91.8\text{ cm}.
Event 2: Randomly selecting a sunflower from the nursery that's shorter than 268.2\text{ cm}.
A data set is approximately normally distributed with mean 2 and standard deviation 2. Both 3.64 and 2.54 are scores from the data set.
Find the value of the z-score that corresponds to a score of 3.64.
Find the value of the z-score that corresponds to a score of 2.54.
State the event that is less likely to occur:
-
Event 1: Randomly selecting a score in the data set greater than 2.54.
Event 2: Randomly selecting a score in the data set greater than 3.64.
State the event that is less likely to occur:
Event 3: Randomly selecting a score in the data set less than 2.54.
-
Event 4: Randomly selecting a score in the data set less than 3.64.
A data set is approximately normally distributed with mean -8 and standard deviation 2. Both -14.86 and -14.4 are scores from the data set.
Find the value of the z-score that corresponds to a score of -14.86.
Find the value of the z-score that corresponds to a score of -14.4
State the event that is more likely to occur:
Event 1: Randomly selecting a score in the data set less than -14.86.
Event 2: Randomly selecting a score in the data set less than -14.4.
State the event that is more likely to occur:
Event 3: Randomly selecting a score in the data set greater than -14.86.
Event 4: Randomly selecting a score in the data set greater than -14.4.
A data set is approximately normally distributed with mean 20 and standard deviation 4.
Complete the table below by finding the rest of the z-scores:
| \text{Scores} | 3.68 | 29.96 | 2.76 | 30.2 |
|---|---|---|---|---|
| z\text{-scores} | -4.08 | 2.49 |
Determine which of the following events is the least likely to occur:
Randomly selecting a score in the data set more than 30.2.
Randomly selecting a score in the data set more than 29.96.
Randomly selecting a score in the data set more than 2.76.
Randomly selecting a score in the data set more than 3.68.
State the event that is less likely to occur:
Event 1: Randomly selecting a score in the data set between 2.76 and 30.2.
Event 2: Randomly selecting a score in the data set between 3.68 and 29.96.
State the event that is more likely to occur:
Event 3: Randomly selecting a score in the data set that is less than 3.68 or greater than 29.96.
Event 4: Randomly selecting a score in the data set that is less than 2.76 or greater than 30.2.
The finish times for a half-marathon are approximately normally distributed. Two runners completed the half-marathon in 151 and 102 minutes respectively. A finish time of 151 minutes has a z-score of 1 and a finish time of 102 minutes has a z-score of - 2.
State the event that is more likely to occur:
Event 1: A randomly chosen runner completed the half-marathon in less than 102 minutes.
-
Event 2: A randomly chosen runner completed the half-marathon in more than 151 minutes.
State the event that is more likely to occur:
Event 3: A randomly chosen runner completed the half-marathon in more than 102 minutes.
-
Event 4: A randomly chosen runner completed the half-marathon in less than 151 minutes.
The amount of time spent waiting in the line at the supermarket checkout is approximately normally distributed.
The z-scores of the waiting times of four customers, represented by the letters K, L, M, and N are given in the table below:
| \text{Customer} | K | L | M | N |
|---|---|---|---|---|
| z\text{-score} | -1.13 | 0.62 | -1.62 | 0.94 |
Determine which of the following events is the least likely to occur:
Waiting longer than N.
Waiting longer than L.
Waiting longer than K.
Waiting longer than M.
State the event that is more likely to occur:
Event 1: Waiting longer than K but less than L.
Event 2: Waiting longer than M but less than N.
State the event that is more likely to occur:
Event 3: Waiting less than K or longer than L.
Event 4: Waiting less than M or longer than N.
The class exam results for a particular subject is approximately normally distributed. The names of four different students along with the z-scores for their exam results are given in the table below:
| \text{Student} | \text{Maximilian} | \text{Tracy} | \text{Neil} | \text{Eileen} |
|---|---|---|---|---|
| z\text{-score} | -2.74 | 1.53 | -2.81 | 1.75 |
It is least likely to randomly select a student that scored higher in the exam than which student?
State the event that is less likely to occur:
Event 1: Randomly selecting a student who scored in the exam between Maximilian and Tracy.
Event 2: Randomly selecting a student who scored in the exam between Neil and Eileen.
State the event that is less likely to occur:
Event 3: Randomly selecting a student who scored less than Neil or greater than Eileen.
Event 4: Randomly selecting a student who scored less than Maximilian or greater than Tracy.
The number of days of sick leave taken by employees is approximately normally distributed. The z-scores of the number of sick days taken by four employees are shown in the table below:
| \text{Employee} | \text{Xavier} | \text{Amelia} | \text{Peter} | \text{Fiona} |
|---|---|---|---|---|
| z\text{-score} | -3.44 | 1.77 | -3.69 | 1.89 |
It is most likely to randomly select an employee who took more sick days than which employee?
State the event that is more likely to occur:
Event 1: Randomly selecting an employee whose sick days were less than Xavier or greater than Amelia.
-
Event 2: Randomly selecting an employee whose sick days were less than Peter or greater than Fiona.
A long-jump athlete performs several attempts in practice, achieving a mean jump of 151 \text{ cm} and a standard deviation of \\24 \text{ cm}. The lengths of two of her attempts and their z-scores are given in the table:
| \text{Length (cm)} | 211 | 71.8 |
|---|---|---|
| z\text{-scores} | 2.5 | -3.3 |
State the event that is more likely to occur:
Event 1: The athlete jumping a length less than 211\text{ cm}.
Event 2: The athlete jumping a length greater than 71.8\text{ cm}.
The number of babies born in a country each day are approximately normally distributed with mean 167 and standard deviation 16. The number of babies born on two consecutive days along with their z-scores are provided below:
| \text{Number of newborns} | 215 | 103 |
|---|---|---|
| z\text{-scores} | 3 | -4 |
State the event that is less likely to occur:
Event 1: The number of babies born the following day is greater than 215.
Event 2: The number of babies born the following day is less than 103.
State the event that is more likely to occur:
Event 1: The number of babies born the following day is less than 215.
Event 2: The number of babies born the following day is greater than 103.
The heights of office buildings in a particular city is approximately normally distributed with mean 55\text{ m} and standard deviation 2\text{ m}. Two particular buildings have heights of 51.3\text{ m} and 51.08\text{ m}.
Find the value of the z-score that corresponds to a height of 51.3\text{ m}.
Find the value of the z-score that corresponds to a height of 51.08\text{ m}.
State the event that is more likely to occur:
Event 1: A randomly chosen building is taller than 51.08\text{ m}.
Event 2: A randomly chosen building is shorter than 51.3\text{ m}.
State the event that is more likely to occur:
Event 3: A randomly chosen building is taller than 51.3\text{ m}.
Event 4: A randomly chosen building is shorter than 51.08\text{ m}.
The lengths of Swordfish are approximately normally distributed with mean 230 \text{ cm} and standard deviation 40 \text{ cm}.
The lengths of recently tagged Swordfish were recorded. Complete the table below by finding the remaining z-scores:
| \text{Lengths (cm)} | 187.6 | 360 | 152 | 379.6 |
|---|---|---|---|---|
| z\text{-scores} | -1.06 | 3.25 |
Determine which of the following events is the least likely to occur:
Capturing a Swordfish that is more than 152\text{ cm}.
Capturing a Swordfish that is more than 379.6 \text{ cm}.
Capturing a Swordfish that is more than 187.6 \text{ cm}.
Capturing a Swordfish that is more than 360\text{ cm}.
State the event that is less likely to occur:
Event 1: Capturing a Swordfish that is between 187.6\text{ cm} and 360\text{ cm}.
Event 2: Capturing a swordfish that is between 152 \text{ cm} and 379.6\text{ cm}.
State the event that is more likely to occur:
Event 3: Capturing a Swordfish that is less than 152\text{ cm} or greater than 379.6\text{ cm}.
Event 4: Capturing a swordfish that is less than 187.6 \text{ cm} or greater than 360\text{ cm}.
The profit a restaurant earns each day is approximately normally distributed with mean \$580 and standard deviation \$20. In the last two days, the restaurant profited \$590.40 and \$567.20 respectively.
Find the z-score that corresponds to a profit of \$590.40.
Find the z-score that corresponds to a profit of \$567.20.
State the event that is more likely to occur:
Event 1: The restaurant profits more than \$590.40 today.
Event 2: The restaurant profits less than \$567.20 today.
State the event that is less likely to occur:
Event 3: The restaurant profits less than \$590.40 today.
Event 4: The restaurant profits more than \$567.20 today.
The times at which individuals visit a cafe are recorded every hour. The data set is approximately normally distributed with the busiest time at 10:00 am and a standard deviation of 14 minutes.
Complete the following table by finding the remaining z-scores:
| \text{Times} | \text{10:14 am} | \text{10:28 am} | \text{10:42 am} |
|---|---|---|---|
| z\text{-scores} |
The cafe owner has a limited number of cakes. To maximise their chance of sales, state the 14-minute interval between 10 am and 11 am that they should have the cakes available.
A fast food restaurant records the arrival time of every customer at the drive thru each morning. The data set is approximately normally distributed with the busiest time at 11:00 am and a standard deviation of 22 minutes.
Complete the following table by finding the z-scores of each arrival time:
| \text{Times} | \text{9:54 am} | \text{10:16 am} | \text{10:38 am} |
|---|---|---|---|
| z\text{-scores} |
The restaurant needs to have extra staff on hand during the busiest time period. State the 22-minute interval between 9 am to 11 am that is the busiest.
The arrival time of a particular train is normally distributed with an expected arrival of \text{} \\5:00 pm and a standard deviation of 14 minutes.
Complete the following table by finding the remaining z-scores:
| \text{Times} | \text{4:32 pm} | \text{5:14 pm} | \text{5:42 pm} |
|---|---|---|---|
| z\text{-scores} |
The train scheduled to arrive at 5:00 pm. State the 28-minute time interval between 4 pm to 5 pm in which the train will most likely arrive.
A data set is approximately normally distributed with a standard deviation of 1. Both 10.07 and 10.3 are scores from the data set. The value of 10.07 has a z-score of 4.07.
What is the mean of the data set?
Find the value of the z-score that corresponds to a score of 10.3.
State the event that is more likely to occur:
-
Event 1: Randomly selecting a score in the dataset greater than 10.07.
Event 2: Randomly selecting a score in the dataset greater than 10.3.
State the event that is more likely to occur:
Event 3: Randomly selecting a score in the dataset less than 10.3.
Event 4: Randomly selecting a score in the dataset less than 10.07.
The amount of soft drink in a can is normally distributed with standard deviation 0.4\text{ mL}. Two cans contain 373.96\text{ mL} and 374.04\text{ mL} of soft drink. A can with 373.96\text{ mL} of soft drink has a \\ z-score of -2.6.
What is the average volume of soft drink in a can?
Find the z-score for a can with 374.04\text{ mL} of soft drink.
State the event that is more likely to occur:
Event 1: Purchasing a can of soft drink with less than 374.04 \text{ mL}.
Event 2: Purchasing a can of soft drink with less than 373.96\text{ mL}.
State the event that is more likely to occur:
Event 3: Purchasing a can of soft drink with more than 374.04\text{ mL}.
Event 4: Purchasing a can of soft drink with more than 373.96\text{ mL}.
Sharon owns a farm with pet chickens. The number of eggs the chickens lay on a given day is approximately normally distributed with standard deviation 9.
On Monday, the chickens laid 116 eggs which has a z-score of 3. What is the average number of eggs the chickens lay on a given day?
Complete the table by finding the rest of the z-scores:
| Monday | Tuesday | Wednesday | Thursday | |
|---|---|---|---|---|
| \text{Eggs} | 116 | 125 | 80 | 71 |
| z\text{-scores} | 3 | 4 |
Next week, Sharon wants to bake cakes for a work function using the eggs laid that will be laid tomorrow. How many eggs is Sharon most likely to obtain: between 116 to 125 or between 71 to 80?
The time it takes for an athlete to complete the bicycle stage of a triathlon is approximately normally distributed with standard deviation 10 minutes. The elapsed times for two athletes at each stage is recorded in the table below:
| \text{Athlete } 1 | \text{Swim (mins)} | \text{Bicycle (mins)} | \text{Run (mins)} |
|---|---|---|---|
| \text{Deborah} | 47 | 134 | 202 |
| \text{Bianca} | 49 | 137 | 201 |
The time it takes Deborah to complete the bicycle stage has a z-score of 0.5. Find the average time it takes for an athlete to complete the bicycle stage of the triathlon.
Find the z-score for the time it takes Bianca to complete the bicycle stage of the triathlon.
State the event that is less likely to occur:
Event 1: Randomly choosing an athlete that completed the bicycle stage slower than 88 minutes.
Event 2: Randomly choosing an athlete that completed the bicycle stage slower than 87 minutes.
State the event that is less likely to occur:
-
Event 3: Randomly choosing an athlete that completed the bicycle stage quicker than 88 minutes.
Event 4: Randomly choosing an athlete that completed the bicycle stage quicker than 87 minutes.
The number of coffees a cafe sells in a weekday is approximately normally distributed with a standard deviation of 9 coffees.
On Monday, the cafe sells 144 cups of coffee which has a z-score of 3. Find the average number of coffees the cafe sells on a weekday.
Complete the following table by finding the rest of the z-scores:
| Monday | Tuesday | Wednesday | Thursday | |
|---|---|---|---|---|
| \text{Coffees} | 144 | 153 | 99 | 90 |
| z\text{-scores} | 3 | 4 |
State the event that is more likely to occur:
Event 1: On a Friday, the number of coffees sold by the cafe will be between 90 and 153.
Event 2: On a Friday, the number of coffees sold by the cafe will be between 99 and 144.
State the event that is more likely to occur:
Event 3: On a Friday, the number of coffees sold by the cafe will be more than 144.
Event 4: On a Friday, the number of coffees sold by the cafe will be more than 153.
Event 5: On a Friday, the number of coffees sold by the cafe will be more than 90.
Event 6: On a Friday, the number of coffees sold by the cafe will be more than 99.