6.5.7-T Assigned Media The overhead reach distances of adult females are normall

Question

6.5.7-T Assigned Media The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8 cm a. Find the probability that an individual distance is greater than 215.50 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 204.00 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is 1056 (Round to four decimal places as needed.) b. The probability is (Round to four decimal places as needed.)

Explanation / Answer

Answer to part b)

Given information:

.

To find P( x> 204)

P(x > 204) = 1 - P(x < 204)

.

The formula of Z is as follows:

Z = (x - M) / (SD / sqrt(n))

.

On plugging the values we get:

Z = (204 -205.5) / (8 /sqrt(15))

Z = -0.7262

.

P(x < 204) = P(z < -0.73) = 0.2327

.

P(x > 204) = 1 - 0.2327 = 0.7673

Thus probability of mean greater than 204 is 0.7673

.

Answer to part c)

This is because the population follows the normal distrbution and the population standard deviation Sigma = 8 is provided is the question. When sigma is known, then we use Z distribution even if the sample size is small.

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