Below are the means and standard deviations of approximately normally distributed data sets. Find the corresponding z-score of the value that comes from each data set:
Mean =2, standard deviation =3, value =5.
Mean =5, standard deviation =2, value =9.
Mean =5, standard deviation =9, value =32.
Mean =5, standard deviation =4, value =1.
Mean =-1, standard deviation =4, value =-5.
Mean =-4, standard deviation =2, value =-2.
Mean =-7, standard deviation =4, value =-19.
Mean =2.2, standard deviation =3.5, value =-3.05.
The marks in a recent English exam are approximately normally distributed with mean 53 and standard deviation 4.
Find the value of the z-score that corresponds to an English mark of 45.
A data set is approximately normally distributed.
If a value that belongs to the data set has a z-score of 4, how many standard deviation(s) is the value away from the mean?
Is the value above or below the mean?
A data set is approximately normally distributed.
If a value that belongs to the data set has a z-score of -1, how many standard deviation(s) is the value away from the mean?
Is the value above or below the mean?
A data set is approximately normally distributed.
If a value that belongs to the data set has a z-score of 2.89, how many standard deviation(s) is the value away from the mean?
Is the value above or below the mean?
For each approximately normally distributed data set below, we are given the standard deviation, a value from the data set and its corresponding z-score. Determine the mean of each data set:
Standard deviation =6, value =11, z-score =1.
Standard deviation =2, value =-1, z-score =2.
Standard deviation =4, value =-3, z-score =-2.
Standard deviation =9.5, value =-15.4, z-score =-0.8.
Standard deviation =9, value =19, z-score =3.
Standard deviation =8, value =-15, z-score =-3.
Standard deviation =4.3, value =21.46, z-score =3.2.
For each approximately normally distributed data set below, we are given the mean, a value from the data set and its corresponding z-score. Determine the standard deviation of each data set:
Mean =3, value =10, z-score =1.
Mean =4, value =-1, z-score =-1.
Mean =-2, value =-7, z-score =-1.
Mean =7.3, value =21.38, z-score =3.2.
Mean =6, value =-3, z-score =-3.
Mean =-6, value =15, z-score =3.
Mean =8.8, value =33.12, z-score =3.2.
A data set is approximately normally distributed with mean \overline{x} and standard deviation s. Find the z-score that corresponds to each of the following values:
\overline{x}+s
\overline{x}+2s
\overline{x}-3s
A data set is approximately normally distributed with mean 275 and standard deviation 44.
What is the mean of the set of z-scores that come from the data set?
What is the standard deviation of the set of z-scores that come from the data set?
A data set is approximately normally distributed with a certain mean and standard deviation.
What is the mean of the set of z-scores that come from the data set?
What is the standard deviation of the set of z-scores that come from the data set?
The amount of food (in kilograms) that goes to waste at a particular restaurant each week is approximately normally distributed with mean unknown and standard deviation 4\text{ kg}.
One week, the restaurant wastes 79\text{ kg} of food, which has a z-score of 3. What is the average amount of waste the restaurant produces each week?
The heights of emus are approximately normally distributed with mean 194\text{ cm} and standard deviation unknown.
If an emu's height is 171.75\text{ cm}, and has a z-score of - 2.5, what is the value of the standard deviation in centimetres?
The number of successful free throws a basketball team makes each game is approximately normally distributed with mean 24 and standard deviation 2.
Find the number of successful free throws which is 2 standard deviations above the mean.
Find the value of the z-score that corresponds to the number of successful free throws found in part (a).
The volume of bottled water is approximately normally distributed with mean 500\text{ mL} and standard deviation 0.5\text{ mL}.
Find the volume of water which is 2.2 standard deviations below the mean.
Find the value of the z-score that corresponds to the volume of water found in part (a).
The heights of a group of Year 12 students (in centimetres) are approximately normally distributed. The heights are shown below:
163, \, 166, \, 159, \, 162, \, 168, \, 167, \, 166, \, 163, \, 162, \, 163
Given that the mean is 163.9\text{ cm }and the standard deviation is approximately 2.62\text{ cm}, calculate the following z-scores to two decimal places:
| \text{Height (cm)} | 159 | 162 | 162 | 163 | 163 | 163 | 166 | 166 | 167 | 168 |
|---|---|---|---|---|---|---|---|---|---|---|
| z-\text{scores} |
What is the mean of the z-scores correct to the nearest integer?
What is the standard deviation of the z-scores correct to the nearest integer?
Is the following statement true or false?
"All data sets that are approximately normally distributed have z-scores with a mean of 0 and a standard deviation of 1."
The number of runs scored by Mario in each cricket match is approximately normally distributed. His runs are shown below:
49, \, 56, \, 48, \, 49, \, 48, \, 45, \, 45, \, 48, \, 40, \, 55
What was his average number of runs correct to two decimal places?
What was his standard deviation correct to two decimal places?
Calculate the following z-scores to two decimal places:
| \text{Runs} | 40 | 45 | 45 | 48 | 48 | 48 | 49 | 49 | 55 | 56 |
|---|---|---|---|---|---|---|---|---|---|---|
| z-\text{scores} |
What is the mean of the z-scores correct to the nearest integer?
What is the standard deviation of the z-scores correct to the nearest integer?