Question

A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80 . Suppose also that exactly 10% of the scores exceed 750 . Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place 7. suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of 0.2 inches and a standard deviation of 0.05 inches. What proportion of woodlice have antenna lengths that are less than 0.15 inches? Round your answer to at least four decimal places. 8. In a certain city of several million people, 6.8% of the adults are unemployed. If a random sample of 240 adults in this city is selected, approximate the probability that at most 14 in the sample are unemployed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.)

Answer 1

6) P(X > 750) = 0.1

Or P((X - )/ > (750 - )/) = 0.1

Or, P(Z > (750 - )/80) = 0.1

Or, P(Z < (750 - )/80) = 0.9

Or, (750 - )/80 = 1.28

Or, 750 - = 1.28 * 80

Or, = 750 - 1.28 * 80

Or, = 647.6

7) P(X < 0.15)

= P((X - )/ < (0.15 - )/)

= P(Z < (0.15 - 0.2)/0.05)

= P(Z < -1)

= 0.1587

8) n = 240

P = 0.068

= n * P = 240 * 0.068 = 16.32

= sqrt(np(1 - p))

= sqrt(240 * 0.068 * (1 - 0.068))

= 3.9

P(X < 14)

= P((X - )/< (14.5 - )/)

= P(Z < (14.5 - 16.32)/3.9)

= P(Z < -0.47)

= 0.3192