Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The incomes of trainees at a local factory are normally distributed with a mean

ID: 3181980 • Letter: T

Question

The incomes of trainees at a local factory are normally distributed with a mean of $1100 and a standard deviation of $150. What is the probability the mean salary of 10 randomly selected trainees is more than $1000 a month? Assume that woman's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 20 women are randomly selected, a) Find the probability that they have a mean height between 62.5 inches and 64.5 inches. b) Find the probability that they have a mean height less than 62.5 inches or more than 64.5 inches.

Explanation / Answer

from normal distribution z=(X-mean)/std deviation

7) std deviation of mean =std deviation/(n)1/2 =47.434

hence P(X>1000)=1-P(Z<(1000-1100)/474.34)=1-P(Z<-2.1082)=1-0.0175=0.9825

8)for std deviation of mean =0.559

a)P(62.5<X<64.5)=P(-1.9677<Z<1.61)=0.9463-0.0245=0.9217

b)P(X<62.5)+P(X>64.5)=1-P(62.5<X<64.5)=1-0.9217=0.0783