Complete the following statements for a normal distribution:
⬚\% of the scores lie within 1 standard deviation of the mean.
⬚\% of the scores lie within 2 standard deviations of the mean.
⬚\% of the scores lie within 3 standard deviations of the mean.
In a normal distribution, approximately what percentage of scores lie:
Between the mean and 1 standard deviation below the mean?
Between the mean and 2 standard deviations above the mean?
Between the mean and 3 standard deviations below the mean?
Draw a normal distribution curve and shade the region that describes:
68\% of the scores that is symmetric about the mean.
95\% of the scores that is symmetric about the mean.
99.7\% of the scores that is symmetric about the mean.
Consider each normal distribution shown below. Each unit on the horizontal axis indicates 1 standard deviation. For each normal distribution, state the approximate percentage of scores that lie in the shaded region:
Draw a normal distribution and shade the region that describes:
The top 16\% of scores
The bottom 2.5\% of scores
In a normal distribution, approximately what percentage of scores lie between:
1 standard deviation above and 2 standard deviations below the mean?
1 standard deviation above and 3 standard deviations below the mean?
2 standard deviations above and 3 standard deviations below the mean?
The grades in a test are approximately normally distributed. The mean mark is 54 with a standard deviation of 10. Between which two scores do the following percentages of results lie symmetrically about the mean?
68\%
95\%
99.7\%
The following figure shows the approximate percentage of scores lying within various standard deviations from the mean of a normal distribution. A set of scores is found to follow such a distribution, where the mean score is 81 and standard deviation is 15. Calculate each of the following using the given values. Find the percentage of scores between:
66 and 96
51 and 111
36 and 126
81 and 96
96 and 111
For a set of scores, it was found that the mean score was 77 and the standard deviation was 15. If the distribution of scores is approximately normal, find the percentage of scores that lie between:
62 and 92
47 and 107
32 and 122
77 and 92
92 and 107
The marks in a class are approximately normally distributed. If the mean mark was 43 with a standard deviation of 6, approximately what percentage of students achieved:
A mark above the average?
A mark above 37?
A mark above 49?
A mark below 31?
A mark above 25?
A mark between 25 and 43?
A mark between 49 and 55?
The high jump results of 600 students in a sports carnival are found to approximately follow a normal distribution, with a mean height of 140\text{ cm} and a standard deviation of 15\text{ cm}. Find the number of heights, to the nearest integer, between:
125\text{ cm} and 155\text{ cm}
110\text{ cm} and 170\text{ cm}
95\text{ cm} and 185\text{ cm}
140\text{ cm} and 155\text{ cm}
155\text{ cm} and 170\text{ cm}
The times that a class of students spent talking or texting on their phones on a particular weekend is approximately normally distributed with mean time of 180 minutes and standard deviation of 7 minutes. Approximately what percentage of students used their phones for between 173 and 187 minutes on the weekend?
The exams scores of students are approximately normally distributed with a mean score of 69 and a standard deviation of 5.
Approximately what percentage of students scored between 59 and 84?
There are 410 students in the class. If the passing score is 59, approximately how many students passed? Give your answer to the nearest integer.
The number of biscuits packaged in biscuit boxes are approximately normally distributed with mean 40 and standard deviation of 5.
Approximately 97.35\% of the boxes lie between 3 standard deviations below and how many standard deviation(s) above the mean?
What is the least and most number of biscuits that the 97.35\% of boxes in part (a) will contain?
The weights of an adult harp seals are approximately normally distributed with mean 142\text{ kg} and standard deviation of 5\text{ kg}.
Approximately 81.5\% of adult harp seals lie between 2 standard deviations below and how many standard deviation(s) above the mean?
What is the range of weights of the 81.5\% of adult males in part (a)?
The times for runners to complete a 100\text{ m} race are approximately normally distributed with mean 15 seconds and standard deviation of 2.3 seconds.
Approximately 81.5\% of people lie between 2 standard deviations below and how many standard deviation(s) above the mean?
What is the range of times in which the 81.5\% of people in part (a) complete the race?
The heights of players in a soccer club are approximately normally distributed, with mean height 1.77\text{ m} and standard deviation 9\text{ cm}. If 500 players are chosen at random, approximately how many players will be taller than 1.5\text{ m}? Round your answer to the nearest integer.
The numbers of biscuits packaged in biscuit boxes are approximately normally distributed with mean 32 and standard deviation 5.
If 5000 boxes of biscuits are produced, approximately how many boxes have more than 17 biscuits? Round your answer to the nearest integer.
The times that professional divers can hold their breath are approximately normally distributed with mean 128 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 104 seconds? Round your answer to the nearest integer.
The operating times of phone batteries are approximately normally distributed with mean 24 hours and a standard deviation of 6 hours.
Approximately what percentage of batteries last between 18 and 42 hours?
Approximately what percentage of batteries last between 12 hours and 42 hours?
Any battery that lasts less than 18 hours is deemed faulty. If a company manufactured 63\,000 batteries, approximately how many batteries would they be able to sell? Round your answer to the nearest integer.
The heights of sunflowers are approximately normally distributed, with a mean height of 1.4\text{ m} and a standard deviation of 5\text{ cm}.
Approximately what percentage of sunflowers are between 1.3\text{ m} and 1.45\text{ m} tall?
Approximately what percentage of sunflowers are between 1.25\text{ m} and 1.45\text{ m} tall?
If there are 4800 sunflowers in the field, approximately how many are taller than 1.3\text{ m}? Round your answer to the nearest integer.
The heights of 800 netball players were measured and found to fit a normal distribution. The mean height is 153\text{ cm} and the standard deviation is 16 \text{ cm}. Find the number of players, to the nearest integer, that would be expected to have a height between:
137 \text{ cm} and 169 \text{ cm}
121\text{ cm} and 185\text{ cm}
105\text{ cm} and 201\text{ cm}
153\text{ cm} and 169\text{ cm}
169\text{ cm} and 185 \text{ cm}