MAP4C The Normal Distribution Homework

  1. Which normal distribution has the highest standard deviation and which has the lowest? Explain.

  1. The marks on a recent test are normally distributed, with mean 72 and standard deviation 6.

a) Determine the marks that are each distance away from the mean:
i) 1 standard deviation
ii) 2 standard deviations
iii) 3 standard deviations
b) Sketch a normal curve. Label the mean and the marks that are 1, 2, and 3 standard deviations

from the mean. Show the percent of data that lie in each interval.

  1. Three sets of data are described. Match each data set with the graph most likely to represent its distribution. Use each graph only once. Explain your pairings.

a) the actual volume of pop in a 1-L bottle
b) the annual incomes of all Canadians over the age of 15
c) the marks received by a group of mathematics students on a chapter test.

  1. The usable lifetimes of 10 000 AA batteries are normally distributed with a mean lifetime of 25 h and a standard deviation of 2 h.

a) Determine the lifetimes that are within 1, 2, and 3 standard deviations of the mean.

b) What percent of batteries have a usable lifetime in each range?

i) between 23 h and 27 h
ii) between 29 h and 31 h
iii) between 19 h and 27 h

  1. The masses of the stones in a load of gravel are normally distributed, with mean 4.8 g and standard deviation 0.4 g.


a) Sketch the normal distribution of the masses of the stones. Label the mean and the points that are 1, 2, and 3 standard deviations from the mean.


b) What percent of the stones have mass in each range?

i) less than 3.6 g ii) greater than 3.6 g

iii) greater than 4.4 g iv) between 4.8 g and 5.2 g

v) between 3.6 g and 6.0 g

  1. The results of a standardized test were normally distributed, with mean 504 and standard deviation 110.


a) Sketch the normal distribution of the test scores. Label the mean and the points that are 1, 2, and 3 standard deviations from the mean.


b) What percent of students had scores in each range?

i) less than 614 ii) greater than 3.6 g

iii) greater than 284 iv) between 394 and 724

c) Estimate the range of test scores.

  1. Sketch each pair of normal distributions on the same grid. How are the sketches similar? How are they different?

a) mean 50, standard deviation 10 b) mean 40, standard deviation 5
mean 50, standard deviation 20 mean 50, standard deviation 5

  1. The Stanford-Binet Intelligence Quotient (IQ) test scores of Canadians are normally distributed, with mean 100 and standard deviation 16.


a) What percent of people have an IQ greater than 132 as measured by this test?


b) The label “genius” applies to a person who scores in the top 2% of all those taking the test. What score would a person need to be classified a genius?

  1. A manufacturer of light bulbs advertises that its light bulbs have a lifetime of 2000 h. An independent research agency tests the light bulbs and finds the lifetimes are normally distributed, with mean 2066.8 h and standard deviation 84.4 h. Is the manufacturer’s claim reasonable?


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