ALLIED MAT130 MODULE 4 check your understanding

Question Points

1.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.

A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers.

a. 0.1003

b. 0.0694

c. 0.9306

d. 0.8997

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2. The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of fewer than 43 democrats.

a. The area to the left of 43.5

b. The area to the left of 42.5

c. The area to the right of 43.5

d. The area to the left of 43

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3. Solve the problem. The following confidence interval is obtained for a population proportion, p: 0.883 < p < 0.911. Use these confidence interval limits to find the margin of error, E.

a. 0.014

b. 0.015

c. 0.897

d. 0.028

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4. Solve the problem. The amount of snowfall in a certain mountain range is normally distributed with a mean of 74 inches, and a standard deviation of 12 inches. What is the probability that the mean annual snowfall during 36 randomly picked years will exceed 76.8 inches?

a. 0.0026

b. 0.0808

c. 0.5808

d. 0.4192

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5. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 90% confidence; n = 300, x = 50

a. 0.0354

b. 0.0443

c. 0.0422

d. 0.0380

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6. A final exam in Math 160 has a mean of 73 with a standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 78.

a. 0.0008

b. 0.8962

c. 0.0036

d. 0.0103

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7. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 95% confidence; n = 2448, x = 1763

a. 0.0151

b. 0.0199

c. 0.0240

d. 0.0178

.

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8. Solve the problem. A final exam in Math 160 has a mean of 73 with a standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 76.

a. 0.8962

b. 0.0301

c. 0.9699

d. 0.9203

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9. Find the indicated probability. The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

a. 97.72%

b. 2.28%

c. 37.45%

d. 47.72%

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10. Of 84 adults selected randomly from one town, 62 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance.

a. 0.659 < p < 0.817

b. 0.626 < p < 0.850

c. 0.615 < p < 0.862

d. 0.644 < p < 0.832

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11. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 130, x = 65; 90%

a. 0.426 < p < 0.574

b. 0.428 < p < 0.572

c. 0.432 < p < 0.568

d. 0.430 < p < 0.570

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12. Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years.

a. 0.4357

b. 0.0714

c. 0.4286

d. 0.0643

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13. Use the normal distribution to approximate the desired probability. A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?

a. 0.4418, no

b. 0.0582, no

c. 0.4418, yes

d. 0.0582, yes

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14. Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. The duration of telephone calls directed by a local telephone company: = 4.2 minutes, n = 500, 97% confidence. Round your answer to the nearest thousandth.

a. 0.009 min

b. 0.018 min

c. 0.408 min

d. 0.087 min

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15. Use the given information to compute a confidence interval for the population mean. 95% confidence; n = 32, = 137, = 2.3

a. 136.0 < < 138.1

b. 132.2 < < 137.8

c. 134.8 < < 139.2

d. 131.9 < < 138.1