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?

2) The amount of time a bank teller spends with each customer has a population mean m = 3.10 minutes and standard deviation s = 0.40 minute. If a random sample of 16 customers is selected.

What is the distribution of the mean amount of time for the samples?

What is the probability that the average time spent per customer will be at least 3 minutes?

There is an 85% chance that the sample mean will be below how many minutes?

If a random sample of 64 customers is selected, there is an 85% chance that the sample mean will be below how many minutes?

*for the solution for problem 2 please say how to do in excel using phstat?

Answer 1

A)

z score given by

so, z=(13000-10000)/2000

=1.5

the probability that John's commission from the jewelry store is less than $13,000 ,P(X<13000) = (Z<1.5)

=0.9331 { =NORMSDIST(1.5)}

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B)

probability that John's commission from the jewelry store is at least $12,000

z- score=(12000-10000)/2000 = 1

P(X>=12000) = P(Z >= 1)

=0.1587

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c)

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

z score for 11000=

Z=(11000-10000)/2000 = 0.5

z score for 12000 = 1

P(11000<X<12000) = P( 0.5<Z <1)

=0.1499

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d)

Probability is 0.95

critical Z -score for probability 0.95 = 1.65 {from z distribution table)

P(Z<1.65) = 0.95

also we know , P(Z > -1.65) =0.95

now,

-1.65 = (X - 10000) / 2000

X= -3300+10000

X=6700

so,the probability is 0.95 that John's commission from the jewelry store is at least $6700 in a given month

________________________________________

e)

probability is 0.75

z score correponding t0 probability 0.75 is 0.674

so,P(Z<0.674) = 0.75

now,0.674 = ( X - 10000)/2000

X=$11348

the probability is 0.75 that John's commission from the jewelry store is less than $11348 in a given month