1 answer

Problem #6: The weight of a sophisticated running shoe is normally distributed with a mean of...

Question:

Problem #6: The weight of a sophisticated running shoe is normally distributed with a mean of 14 ounces. (a) What must the st

Problem #6: The weight of a sophisticated running shoe is normally distributed with a mean of 14 ounces. (a) What must the standard deviation of weight be in order for the company to state that 95% of its shoes weight less than 15 ounces? (b) Suppose that the standard deviation is actually 0.83. If we sample 8 such running shoes, find the probability that exactly 4 of those shoes weigh more than 15 ounces. Problem #6(a): Round your answer to 2 decimals. Problem #6(b): Round your answer to 4 decimals.

Answers

P(X < A) = P(Z < (A - mean)/standard deviation)

a) Let the standard deviation be \sigma

P(X < 15) = 0.95

P(Z < (15 - 14)/\sigma) = 0.95

From standard normal distribution table, take the value of Z corresponding to 0.95

(14 - 13)/\sigma = 1.96

\sigma = 0.5102

b) P(X > 15) = 1 - P(Z < 15)

= 1 - P(Z < (15 - 14)/0.83)

= 1 - P(Z < 1.20)

= 1 - 0.8849

= 0.1151

P(exactly 4 of those shoes weigh more than 0.1151)

= 8C4 x 0.11514 x 0.88494

= 0.0075

.

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