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
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