The mean of a set of scores is 77 and the standard deviation is 29. Find the value of the following:
\text{Mean } - \text{Standard Deviation}
\text{Mean } + 2 \times \text{Standard Deviation}
\text{Mean } - \dfrac{\left( 2 \times \text{Standard Deviation}\right)}{3}
\text{Mean } + \dfrac{\left( 4 \times \text{Standard Deviation}\right)}{5}
\text{Mean } + 3 \times \text{Standard Deviation}
\text{Mean } - 2 \times \text{Standard Deviation}
For a normal distribution, find the percentage of the scores that lie within:
1 standard deviation of the mean.
2 standard deviations of the mean.
3 standard deviations of the mean.
For a normal distribution, find the percentage of the scores that lie between:
The mean and 1 standard deviation above the mean.
The mean and 2 standard deviations below the mean.
The mean and 3 standard deviations below the mean.
1 standard deviation above and 2 standard deviations below the mean.
1 standard deviation below and 3 standard deviations above the mean.
2 standard deviations below and 3 standard deviations above the mean.
For a normal distribution, the percentage of scores which lie within x standard deviation(s) of the mean are given below. Find the approximate value of x for each percentage:
68\%
95\%
99.7\%
For a normal distribution, the percentage of scores which lie between the mean and x standard deviation(s) above the mean are given below. Find the approximate value of x for each percentage:
34\%
47.5\%
49.85\%
For each normal distribution shown below, each unit on the horizontal axis indicates 1 standard deviation. Find the percentage of scores that lie in each of the shaded regions:
A set of scores is found to follow a normal distribution, where the mean score is 12 and standard deviation is 3.
Sketch the normal distribution representing the distribution of scores.
Find the percentage of scores matching each of the descriptions below and illustrate your answer by shading the associated region under the normal curve:
Scores between 12 and 18.
Scores less than 18.
Scores greater than 9.
A set of scores is found to follow a normal distribution, where the mean score is 92 and standard deviation is 20. Find the percentage of scores that lie between:
72 and 112
52 and 132
32 and 152
92 and 112.
112 and 132
A set of scores is found to follow a normal distribution, where the mean score is 61 and standard deviation is 11. Find the percentage of scores that lie between:
72 and 83
50 and 61
61 and 83
39 and 72
28 and 50
The results from an exam were normally distributed with a mean score of 65 and standard deviation 9:
Find the value of x.
Find the value of y.
The scores in a test were normally distributed with a mean mark of 60 and standard deviation 2. State which two scores the following percentages lie between, if the scores lie symmetrically about the mean:
68\%
95\%
99.7\%
The marks in a class were normally distributed with a mean mark of 47 and standard deviation 6. Find the percentage of students who achieved:
A mark above the average.
A mark above 41.
A mark above 53.
A mark below 35.
A mark above 29.
A mark between 29 and 47.
A mark between 53 and 59.
The times that a class of students spent talking or texting on their phones on a particular weekend is normally distributed with mean time 173 minutes and standard deviation 4 minutes.
State the percentage of students that used their phones for between 165 and 181 minutes on the weekend.
One of the world’s largest earthworms is a species found in Gippsland and its length is normally distributed with a mean length of 90 \text{ cm} and standard deviation of 15 \text{ cm}.
Sketch the normal distribution of the lengths of the earthworms.
Find the percentage of worms matching each of the descriptions below and illustrate your answer by shading the associated region under the normal curve:
Between 75 \text{ cm} and 105 \text{ cm}.
Less than 60 \text{ cm}.
Greater than 105 \text{ cm}.
If 200 worms are dug up at random, how many would you expect to be greater than 105 \text{ cm}?
The heights of 400 netball players were measured and found to fit a normal distribution. The mean height is 149 \text{ cm} and the standard deviation is 11 \text{ cm}. Find the number of players that would be expected to have a height between:
138 \text{ cm} and 160 \text{ cm}
127 \text{ cm} and 171 \text{ cm}
116 \text{ cm} and 182 \text{ cm}
149 \text{ cm} and 160 \text{ cm}
160 \text{ cm} and 171 \text{ cm}
The heights of 600 boys are found to follow a normal distribution, with a mean height of 145 \text{ cm} and a standard deviation of 20 \text{ cm}. Find the number of boys that would be expected to have a height between:
125 \text{ cm} and 165 \text{ cm}
105 \text{ cm} and 185 \text{ cm}
85 \text{ cm} and 205 \text{ cm}
145 \text{ cm} and 165 \text{ cm}
165 \text{ cm} and 185 \text{ cm}
The number of biscuits in a box is normally distributed with a mean of 30 and standard deviation of 3.
Approximately 81.5\% of the boxes contain between 2 standard deviations below and x standard deviation(s) above the mean. Find the value of x.
Hence, state the numbers of biscuits per box that approximately 81.5\% of the boxes would lie between.
The weights of an adult harp seals are normally distributed with mean 144 \text{ kg} and standard deviation of 6 \text{ kg}.
Approximately 83.85\% of adult harp seals lie between 1 standard deviation below and x standard deviation(s) above the mean. Find the value of x.
Hence, state the weights in kilograms that approximately 83.85\% of the adult males seals would lie between.
The times for runners to complete a 100 \text{ m} race is normally distributed with a mean of 14 seconds and standard deviation of 1.9 seconds.
Approximately 97.35\% of people lie between 3 standard deviations below and x standard deviation(s) above the mean. Find the value of x.
Hence, state the times in seconds that approximately 97.35\% of the runners' completion times would lie between.
The height of sunflowers are normally distributed, with a mean height of 1.6 \text{ m} and a standard deviation of 5 \text{ cm}.
Find the percentage of sunflowers that are between 1.5 \text{ m} and 1.75 \text{ m} tall.
Find the percentage of sunflowers that are between 1.55 \text{ m} and 1.75 \text{ m} tall.
If there are 3000 sunflowers in the field, approximately how many are taller than 1.5 \text{ m}?
The exams scores of students are normally distributed with a mean score of 63 and a standard deviation of 8.
Find the percentage of students that scored between 39 and 79.
There are 450 students in the class. If the passing score is 39, approximately how many students passed?
The operating times of phone batteries are normally distributed with mean 34 hours and a standard deviation of 4 hours.
State the percentage of batteries that last between 22 hours and 42 hours.
State the percentage of batteries that last between 30 hours and 42 hours.
Any battery that lasts less than 22 hours is deemed faulty. If a company manufactured 51\,000 batteries, approximately how many batteries would they be able to sell?
The number of biscuits packaged in biscuit boxes is normally distributed with mean 38 and standard deviation 5. If 4000 boxes of biscuits are produced, approximately how many boxes have more than 33 biscuits?
The heights of players in a soccer club are normally distributed, with mean height 1.76 \text{ m} and standard deviation 5 \text{ cm}. If 700 players are chosen at random, approximately how many players will be taller than 1.66 \text{ m}?
The times that professional divers can hold their breath are normally distributed with mean 236 seconds and standard deviation 12 seconds. If 700 professional divers are selected at random, approximately how many would be able to hold their breath for longer than 200 seconds?