The overhead reach distances of adult females are normally distributed with a me

Question

The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.6 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 distance is greater than 203.30 cm. C. Why can the normal distribution be used in part (b), even through the sample size does not exceed 30? The probability is b. The probability is (Round to four decimal places as needed.) choose the correct answer below. A. The normal distributed can be used because the original population has a normal distributed The normal distribution can be used because the mean is large. The normal distribution can be used because the finite population correction factor is small. D. The normal distribution can be used because the probability is less than 0.5.

Explanation / Answer

SolA:

mean=205.5

stddev=8.6

P(X>215.5)

z=x-mean/sd

=215.5-205.5/8.6

=1.163

P(Z>1.163)

P ( Z>1.163 )=1P ( Z<1.163 )=10.877=0.123

ANSWER :0.123

SOLIUTIONB:

P(X>203.3)

n=15

z=203.3-205.5/8.6/sqrt(15)

=-0.99

P(Z>-0.99)

P ( Z>0.99 )=P ( Z<0.99 )=0.8389

ANSWER:0.8389

SOLUTIONC:

OPTIONA

NORMAL DISTRIBUTION USED SINCE ORIGINAL POPULATION HAS NORMAL DISTRIBUTION

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