Question

The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 7.8 cm.

a. Find the probability that an individual distance is greater than 210.00 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 198.50 cm.

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

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	200
std deviation   =σ=	7.800

probability =P(X>210)=P(Z>(210-200)/7.8)=P(Z>1.28)=1-P(Z<1.28)=1-0.8997=0.1003

b)

probability =P(X>198.5)=P(Z>(198.5-200)/2.014)=P(Z>-0.74)=1-P(Z<-0.74)=1-0.2296=0.7704

c)

since population is normally distributed , sampling distribution will be normal distribution irrespective of sample size