Resources

Resources

Find values of normal variables

3

. Scores on the SAT form a normal distribution with

\mu=500

\sigma=100

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a) What is the minimum score necessary to be in the top

15 \%

of the SAT distribution?

Complete the statement. Round your answer to the nearest thousandth.

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In a population that is normally distributed with mean

5

and standard deviation

14

90\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

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In a population that is normally distributed with mean

47

and standard deviation

25

20\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

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In a population that is normally distributed with mean

78

and standard deviation

13

20\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

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In a population that is normally distributed with mean

34

and standard deviation

6

70\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

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In a population that is normally distributed with mean

77

and standard deviation

6

70\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

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In a population that is normally distributed with mean

92

and standard deviation

18

70\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

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In a population that is normally distributed with mean

19

and standard deviation

19

20\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

47

and standard deviation

13

90\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

1

and standard deviation

21

30\%

of the values are those less than ___.

Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

19

and standard deviation

12

10\%

of the values are those less than ___.

Find the critical value

t_{c}

for the confidence level

c=0.80

and sample size

n=9

\newline

t_{c}=\square

(Round to the nearest thousandth as needed.)

Use the confidence interval to find the margin of error and the sample mean.

\newline

(1.57,2.15)

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The margin of error is

\newline

(Round to two decimal places as needed.)

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The sample mean is

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(Type an integer or a decimal.)

Some states now allow online gambling. As a marketing manager for a casino, you need to determine the percentage of adults in those states who gamble online. How many adults must you survey in order to be

90\%

confident that your estimate is in error by no more than one percentage point? Complete parts (a) and (b) below.

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(a). Assume that nothing is known about the percentage of adults who gamble online.

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n=6766

\newline

(Round up to the nearest integer.)

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(b). Assume that

18\%

of all adults gamble online.

\newline

n=\square

\newline

(Round up to the nearest integer.)

Find the critical value

z_{\alpha/2}

that corresponds to the given confidence level.

\newline

99

\newline

z_{\alpha/2}=\square

(Round to two decimal places as needed.).

For the following set of data, find the population standard deviation, to the nearest hundredth.

\newline

139, 126, 51, 61, 77, 109, 112

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For the following set of data, find the sample standard deviation, to the nearest thousandth.

\newline

59,68,40,56,36,70,20

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For the following set of data, find the sample standard deviation, to the nearest thousandth.

\newline

59,68,40,56,36,70,20

For the following set of data, find the sample standard deviation, to the nearest hundredth.

\newline

40,86,79,25,75,67,86,38

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean

266

days and standard deviation

16

days. Choose two pregnancies independently and at random.

\newline

(a) What is the expected difference in the lengths of the two pregnancies?

Complete the statement. Round your answer to the nearest thousandth.

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In a population that is normally distributed with mean

43

and standard deviation

3

30\%

of the values are those less than ______.