Probability and Statistics

Directions:      Show all relevant work.  No work, no credit.

Distinguish your work from your answers.

TI Calculator use Permitted

 

1. Suppose the hourly wages of all workers in a manufacturer company have a normal distribution with a mean of $15.50 and a standard deviation of $2.75. If we randomly select a sample of 10 workers from this company, find the probability that their mean hourly wage is:
   14. Less than $14.25

 

 

16. More than $16.50

 

2. Suppose the monthly salary of teacher with no more than 5 years teaching experience in California follows a normal distribution with the mean of $6250 and standard deviation of $320.
   1. What is the probability that a randomly selected teacher with no more than 5 years teaching experience in California makes less than $6000 or more than $6500 per month?

 

1. Find a range of salaries, rounded to the nearest ten, that separates the middle 80% from the rest.

 

3. Samsung TV have normal distribution of no repairs time with the mean of 9.5 years and standard deviation of 1.75 years. If we randomly select 1 Samsung TV, find the probability that
   1. No repair is needed between 5 to 9 years.

 

 

1. Find two values that separates the middle 60% from the rest

 

 

8. If we randomly select 4 such TVs, find the probability that their mean is above 8.

 

 

4. A loaded coin with .65 probability of tails is tossed 800 times. Find the following:
   1. n=
   2. p=
   3. q=
   4. μ=
   5. σ2=
   6. σ=
   7. Find P(number of tails is at least 460)

 

 

 

1. Estimate Pnumber of tails is at least 460 using normal distribution.

 

 

 

 

5. Use a uniform probability distribution for all values from 20 to 50.
   1. Draw and label

 

 

1. Find P(x=25)

 

 

 

25. Find P(x<25.5 or x>35)

 

 

1. Find two values that separates the middle 60% from the rest

 

 

6. Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for one winning ticket is to be $500. Find the expected value.

 

 

 

 

7. Given the following probability distribution table,

x	P(x)
1		.12
2
3		.3
4		.23
5		.12

1. Find P(x=2)

 

 

 

1. Draw and label probability distribution histogram

 

 

1. Find μ and σ

 

 

 

1. Find the exact value for σ2

 

 

 

 

 

1. Use one decimal place to find the usual range

 

 

 

8. Suppose there are 10 females and 15 males. Select 3 people.
   1. How many ways can we select 3 people?

 

 

1. How many ways can we select 3 females?

 

 

1. Find P(3 females)

 

 

1. How many ways can we select 2 females? Keep in mind, we must select 3 people.

 

 

 

1. Find P(2F and 1M)

 

 

1. P(1F and 2M)

 

 

1. P(0F and 3M)

 

 

9. Suppose PA=.7, PB=.3, A&B are I.E.
   1. Find P(A and B)

 

 

1. Find P(A or B)

 

 

 

1. Make venn diagram

 

 

1. Find PAB=

 

 

 

1. Find PBA=

 

 

 

 

10. nswer the following questions given the table below .

 

Do you drink?

 

Freq	Yes	No	Total
Males	17	23	40
Females	20	40	60
Total	37	63	100

 

1. Find PMY

 

 

1. Find P(N|F)

 

 

1. Find P(Male or no)