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 202.5 cm and a standard deviation of 7.8 cm a. Find the probability that an individual distance is greater than 215.00 cm. b. Find the probability that the mean for 25 randomly selected distances is greater than 201.20 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 0545 Round to four decimal places as needed.) b. The probability is (Round to four decimal places as needed.)

Explanation / Answer

SolutionA:

use the below R code:

pnorm(215, mean=202.5, sd=7.8, lower.tail=FALSE)

Output:

0.05451546

ANSWER:0.0545

Solutionb:

sample size=25

std error=sample sd/sqrt(n)

=7.8/sqrt(25)

std error=1.56

Rcode is:

pnorm(201.2, mean=202.5, sd=1.56, lower.tail=FALSE)

Output:

0.7976716

ANSWER:0.7977

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