The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 7.8 cm.

Question

a. Find the probability that an individual distance is greater than 204.30cm.

b. Find the probability that the mean for

25 randomly selected distances is greater than 193.70 cm.

a. The probability is ...

​(Round to four decimal places as​ needed.)

b. The probability is ...

​(Round to four decimal places as​ needed.)

Answer 1

mean = 195 cm, standard deviation = 7.8 cm

normal distribution

what is the probability a randomly selected female has a reach greater than 204.3 cm?

calculate the z score

z= (204.3- 195)/7.8 = 9.3/7.8 = 3.1/2.6 = 31/26

z= 31/26 = about 1.1923

use z tables or a z calculator to find the area under the curve between z=0 and z=1.1923

then subtract that area value from 1/2 to get the proportion that is greater than 204.3 cm

multiply by 100 to get the percentage