TOTl0. Time L his Question: 10 pts 1 of 10 (0 complete) TI The overhead reach di

Question

TOTl0. Time L his Question: 10 pts 1 of 10 (0 complete) TI The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 7.8 em a. Find the probability that an individual distance is greater than 218.00 cm b. Find the probability that the mean for 15 randomly selected distances is greater than 203.70 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 302 a. The probability is (Round to four decimal places as needed) b. The probability is Round to four decimal places as needed ) c. Choose the corect answer below O A. The normal distribution can be used because the probability is less than 0.5 O B. The nomal distribution can be used because the fnite population correction factor is small C. The normal distribution can be used because the mean s large O D. The normal distribution can be used because the orgin al population has a normial distnbution

Explanation / Answer

Ans:

mean=205.5

standard deviation=7.8

a)

z=(218-205.5)/7.8

z=1.603

P(z>1.603)=0.0545

b)

z=(203.70-205.5)(7.8/sqrt(15))

z=-0.894

P(z>-0.894)=0.8143

c)Option D is correct.

The normal distribution can be used because the original population has a normal distribution.

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