Question

Question 11: The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last a) less than 7 months. b) between 7 and 12 months. Question 12 The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. a) What percent of people earn less than $40,000 b) What percent of people earn between $45,000 and $65,000? c) What percent of people earn more than $70,000?

Answer 1

Question 11

It is given that the length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Now,

a)We have to find the probability that an instrument produced by this machine will last less than 7 months.

Thus,the required probability is P(x<7)=P[z<(7-12)/2]=P(z<-2.5) =0.0062 (using z-score table)

b)We have to find the probability that an instrument produced by this machine will last between 7 and 12 months.

Thus,the required probability is P(7<x<12)=

P[(7-12)/2<z<(12-12)/2]=P(-2.5<z<0)=0.4938 (using z-score table).