Question

6) A fashion designer would like to do a study to schedule her production. It is known that the ladies' waist has an average of 55.4 cm and a standard deviation of 8.2 cm. If you take a random lady, what is the probability that her waist (length) is
a) Less than 58 cm A=0.6255
b) If samples of 10 young ladies are taken, what is the probability that the average length is more than 50.6 A=0.9678

Answer 1

a)

Given,

= 55.4 , = 8.2

We convert this to standard normal as

P(X < x) = P(Z < x - / )

So,

P(X < 58) = P(Z < 58 - 55.4 / 8.2)

= P(Z < 0.32)

= 0.6255

b)

Using central limit theorem,

P( < x) = P(Z < x - / ( / sqrt(n) ) )

P( > 50.6 ) = P(Z > 50.6 - 55.4 / sqrt(8.2 / sqrt(10) ))

= P(Z > -1.85)

= P(Z < 1.85)

= 0.9678