Question

1. The overhead reach distances of adult females are normally distributed with a mean of 200 cm. and a standard deviation of 8 cm.
   1. Find the probability that an individual’s distance is less than 205cm.
   2. Find the probability that the mean for 25 randomly selected distances is less than 205cm.

Answer 1

Solution :

Given that ,

mean = = 200

standard deviation = = 8

(a)

P(x < 205) = P[(x - ) / < (205 - 200) / 8]

= P(z < 0.625)

= 0.734

(b)

= / n = 8 / 25 = 1.6

P( < 205) = P(( - ) / < (205 - 200) / 1.6)

= P(z < 3.125)

= 0.9991