1) In a roll of film, there are 24 snapshots, but the store does not always print all of them. The following table gives the number of printed pictures and their probabilities:

X | Y

20 |0.12

21 |?

22 |0.49

23 |0.20

24 |0.05

a) Find the missing probability in the table above.(2 decimal places)

b) Find theExpected Valuefor the above table.(2 decimal places)

c) Find theVariancefor the table above.(2 decimal places)

2)

a) Construct aProbability Distributionfor the Experiment of having 5 children where the random variable is the number of boys.Round your answers to 2 decimal places or you will be marked wrong!

(Do not forget to put a ZERO before the decimal for all the probabilities!)

b) Find theExpected Value.

3)

A contractor is considering a new residential project that promises aNETprofit of $5000 with a probability of 0.8, or a loss of $800 (cost of the bid!).

a) Construct the probability distribution.(Round the missing probability to 1 decimal place and complete the table below.)

(DO NOT forget to place a zero before the decimalin the probability column)

X

P

b) Find the mean. (The answer is a whole number!)

c) Find the variance. (The answer is a whole number!)

4) TheNETprizes that can be won in a sweepstakes are listed below together with the chances of winning each one: $3800 (1 chance in 80); $2500 (1 chance in 60); $700 (1 chance in 40); $300 (1 chance in 20). Find theExpected ValueandStandard Deviationof the amount won foroneentry if the cost of entering is$0.85!

a)

(Use 3 decimal places for writing the probabilities in table below!)

(DO NOT forget to place a zero before the decimalin the probability column)

X

P

b) Find theExpected Value.(Round to the nearest whole number)

ExpectedValue =

c) Find theStandard Deviation.(Round to the nearest whole number)

Standard Deviation=

5) If you toss a coin 140 times, what is the probability that you will get exactly 80 tails! (Must use the Binomial Formula once!). Recall that P(tails)=0.5!(Round to 4 decimal places)

(Do not forget to place a ZERO before your decimal numbers)

P(X=80)

=

6) In a study, 38% of adults questioned reported that their health was excellent. Find the probability that when 15 adults are randomly selected,

a) fewer than 3 are in excellent health(Round to 4 decimal places)

(Do not forget to place a ZERO before the decimal)

P(fewer than 3) =

b) at least 5 are in excellent health.(Round to 4 decimal places)

(Do not forget to place a ZERO before the decimal)

P(at least 5) =

c) at most 6 are in excellent health.(Round to 4 decimal places)

(Do not forget to place a ZERO before the decimal)

P(at most 6) =

d) Find the VARIANCE of the distribution.(Round to 2 decimal places)

s2=

7) Find the probability that Z is less than 2.37?(Round your final answer to 4 decimal places)

8)If Z is N(0,1), find the probability that Z lies between 1.05 and 2.36.(Use 4 decimal places for the final answer)

(Do not forget to place a ZERO before the decimal)

9) Find the Probabilities;(Do not forget to place a ZERO before the decimal)

a)P(Z<1.46)

(use 4 decimal places)

b)P(Z>1.64)

(use 4 decimal places)

(Do not forget to place a ZERO before the decimal)

10)

AssumingN(0,1), find the following percentiles!

a) FindP40

.(2 decimal places)

(Do not forget to place a ZERO before the decimal)

b) FindP83

.(2 decimal places)

(Do not forget to place a ZERO before the decimal)

11)

GivenN(62,13),findP99

.(2 decimal places)

(Do not forget to place a ZERO before the decimal)

12)

Suppose that replacement times for timing belts in cars are normally distributed with a mean of 9 years and a standard deviation of 3 years. Find the replacement time that separates the top 12% from the bottom 88%.(2 decimal places for the final answer)

13)

Given N(100,15), findP(X>110)

.(4 decimal places)

(Do not forget to place a ZERO before the decimal)

14)

The volumes of Hemi engines are normally distributed with a mean of 390 cubic inches and a standard deviation of 30 cubic inches. What is the probability that the volume of a randomly selected Hemi engine from the production line will be less than 360 cubic inches?(4 decimal places)

(Do not forget to place a ZERO before the decimal)