Ch. 7 The Normal Probability Distribution
7.1 Properties of the Normal Distribution
1 Use the uniform probability distribution.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 64°F to 92°F. What is the probability that a randomly selected August day has a high temperature that exceeded
69°F?
A) 0.8214
B) 0.1786
C) 0.4423
D) 0.0357
2) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 73°F to 103°F. Find the high temperature which 90% of the August days exceed.
A) 76°F
B) 100°F
C) 83°F…show more content… You randomly sample 30 preschool children and find their weights to be as follows.
25 25 26 26.5 27 27 27.5 28 28 28.5
29 29 30 30 30.5 31 31 32 32.5 32.5
33 33 34 34.5 35 35 37 37 38 38
a) Draw a histogram to display the data. Is it reasonable to assume that the weights are normally distributed? Why?
b) Find the mean and standard deviation of your sample.
c) Is there a high probability that the mean and standard deviation of your sample are consistent with those found in previous studies? Explain your reasoning.
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
2) The graph of a normal curve is given. Use the graph to identify the value of μ and σ.
3
6
A) μ = 12, σ = 3
9
12
15
18
B) μ = 3, σ = 12
21
C) μ = 12, σ = 9
D) μ = 9, σ = 12
3) The normal density curve is symmetric about
A) Its mean
B) The horizontal axis
C) An inflection point
D) A point located one standard deviation from the mean
4) The highest point on the graph of the normal density curve is located at
A) its mean
B) an inflection point
C) μ + σ
D) μ + 3σ
5) Approximately ____% of the area under the normal curve is between μ - 3σ and μ + 3σ.
A) 99.7
B) 68
C) 95
D) 50
Determine whether the graph can represent a normal curve. If it cannot, explain why.
6)
A) The graph cannot represent a normal density function because it increases