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Chapter 6: Q. 6.28 (page 260)

The area under a particular normal curve between 10and 15is 0.6874. A normally distributed variable has the same mean and standard deviation as the parameters for this normal curve. What percentage of all possible observations of the variable lie between 10and 15? Explain your answer.

Short Answer

Expert verified

If the area under the normal curve lies between 10, 15 is 0.6874,then 68.74%of all possible observation of the variable lies between 10, 15.

Step by step solution

01

Step 1. Given Information.

The area under a particular normal curve between 10and 15 is0.6874.

02

Step 2. Find the percentage.

For a normally distributed variable, the value of all possible observations that lie within any specified range equals the corresponding area under its associated normal curve expresssed as percentage.

If the area under the normal curve lies between 10, 15 is 0.6874,then 68.74% of all possible observation of the variable lies between 10, 15.

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Most popular questions from this chapter

We have provided a normal probability plot of data from a sample of a population. In each case, assess the normality of the variable under consideration.

The area under the standard normal curve that lies to the left of a z-score is always strictly between ------ and ------.

A classic study by F. Thorndike on the number of calls to a wrong number appeared in the paper "Applications of Poisson's Probability Summation" (Bell Systems Techical Journal. Vol. 5, pp. 604-624). The study examined the number of calls to a wrong number from coin-box telephones in a large transportation terminal. Based on the results of that paper. we obtained the following percent distribution for the number of wrong numbers during a 1-minute period.

a. Construct a relative-frequency histogram of these wrong-number data.

b. Based on your histogram, do you think that the number of wrong numbers from these coin-box telephones is approximately normally distributed? Explain your answer.

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Female College Students. Refer to Example 6.3 on page 256 .

a. The area under the normal curve with parameters 渭=64.4and蟽=2.4that lies to the left of 61is0.0783. Use this information to estimate the percentage of female students who are shorter than 61inches.

b. Use the relative-frequency distribution in Table 6.1 to obtain the actual percentage of female students who are shorter than 61 inches.

c. Compare your answers from parts (a) and (b).
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