Question

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

200 cm200 cm

and a standard deviation of

7.8 cm7.8 cm.

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

209.30209.30

cm.

b. Find the probability that the mean for

2020

randomly selected distances is greater than 198.70 cm.198.70 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

Answer 1

Solution :

Given that ,

mean = = 200

standard deviation = = 7.8

(a)

P(x > 209.30) = 1 - P(x < 209.30)

= 1 - P[(x - ) / < (209.30 - 200) / 7.8]

= 1 - P(z < 1.19)

= 0.117

(b)

n = 20

= 200

= / n = 7.8 / 20 = 1.7441

P( > 198.70) = 1 - P( < 198.70)

= 1 - P[( - ) / < (198.70 - 200) / 1.7441]

= 1 - P(z < -0.75)

= 1 - 0.2266

= 0.7734

(c)

Original distribution is normal .