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1. John has two jobs. For daytime work at a jewelry store he is paid $15,000 per

ID: 3203143 • Letter: 1

Question

1. John has two jobs. For daytime work at a jewelry store he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with mean $10,000 and standard deviation $2,000. John's income levels from these two sources are independent of each other. Use this information to answer the following questions: a. for a given month, what is the probability that John's commission from the jewelry store is less than $13,000? b. for a given month, what is the probability that John's commission from the jewelry store is at least $12,000? c. for a given month, what is the probability that John's commission from the jewelry store is between $11,000 and $12,000? d. the probability is 0.95 that John's commission from the jewelry store is at least how much in a given month? e. the probability is 0.75 that John's commission from the jewelry store is less than f. how much in a given month?

Explanation / Answer

John has two jobs. For daytime work at a jewelry store he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with mean $10,000 and standard deviation $2,000. John's income levels from these two sources are independent of each other. Use this information to answer the following questions:

a. for a given month, what is the probability that John's commission from the jewelry store is less than $13,000?

Ans:Z=13000-10000/2000

          =1.5

             the probability that John's commission from the jewelry store is less than $13,000 is

      =NORMSDIST(1.5)=0.9331=93.31%

c. for a given month, what is the probability that John's commission from the jewelry store is between $11,000 and $12,000?

Ans:Z=11000-10000/2000
          =0.5

=NORMSDIST(0.5)=0.6914

Z=12000-10000/2000
          =1

=NORMSDIST(1)=0.8413

the probability that John's commission from the jewelry store is between $11,000 and $12,000 is

     0.8413-0.6914

     =0.1499