A survey was conducted to measure the number of hours per week adults in the United States spend on home computers. In the survey, the number of hours was normally distributed, with a mean of 7 hours and a standard deviation of 1 hour. A survey participant is randomly selected. Which of the following statements is true?

(a) The probability that the hours spent on the home computer by the participant are less than 4.5 hours per week is 0.9938.

(b) The probability that the hours spent on the home computer by the participant are between 4.5 and 9.5 hours per week is 0.0124.

(c) The probability that the hours spent on the home computer by the participant are more than 9.5 hours per week is 0.9938.

(d) 0.13% of the adults spend more than 4 hours per week on a home computer.

(e) If 43 adults in the United States are randomly selected, you would expect to say about 1 adult spend less than 5 hours per week on a home computer.

1.) Use the definitions given in the text to find both the odds for and the odds against the following event.

-Flipping 4 fair coins and getting 0 heads.

The odds for getting 0 heads are what to what.​(Type a whole​ number.)

The odds against getting 0 heads are what to what. (Type a whole number)

2.) Determine whether the following individual events are overlapping or​ non-overlapping. Then find the probability of the combined event.

Getting a sum of either 4 or 8 on a roll of two dice

Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.

3.)Determine the probability of having 2 girls and 3 boys in a 5​-child family assuming boys and girls are equally likely.  

The probability of having 2 girls and boy sis is?

4.) Use the​ "at least​ once" rule to find the probabilities of the following event.

Getting at least one head when tossing seven fair coins

1. In a non-transparent bag there are 5 equally-weighted balls, each of them is marked by a number 1,2,3,4 and 5. Now we randomly pick 3 balls out of the bag and we note X as the smallest number among the 3 balls picked. The order is of no importance.(10 pt)
   1. What is the statistic distribution of X?
   2. Compute E(X) and also .

2. Suppose that a factory products the same product using 3 different workshops A, B and C, the producing capacity ratio of these workshops are A: B: C=3:2:1. The failure rates of product produced by these workshops are 8% for workshop A, 9% for workshop B and 12% for workshop C. Now we randomly select a product produced by this factory. (10 pt)
   1. Using conditional probability theory, what is the probability that this product selected is a failure one ?
   2. If the product select is indeed a failure one, what is the probability that it’s produced by workshop A?

6. Create a probability distribution for a coin flipping game. That is, toss a coin at least 25 times and keep up with the number of heads and the number of tails. (8 points for each part) a. Compile your data into a probability distribution. Be sure to show that your distribution meets the properties for a probability distribution.

RESULTS

Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Res. T H H H T H H H H T H H T H T H T T H T T H H T H

H15/25=3/5

T 10/25=2/5

3/5+2/5=1

How do you create a distribution for this?

A survey was conducted to measure the number of hours per week adults in the United States spend on home computers. In the survey, the number of hours was normally distributed, with a mean of 7 hours and a standard deviation of 1 hour. A survey participant is randomly selected. Which of the following statements is true?

(a) The probability that the hours spent on the home computer by the participant are less than 4.5 hours per week is 0.9938.

(b) The probability that the hours spent on the home computer by the participant are between 4.5 and 9.5 hours per week is 0.0124.

(c) The probability that the hours spent on the home computer by the participant are more than 9.5 hours per week is 0.9938.

(d) 0.13% of the adults spend more than 4 hours per week on a home computer. (e) If 43 adults in the United States are randomly selected, you would expect to say about 1 adult spend less than 5 hours per week on a home computer.

In analyzing hits by bombs in a past war, a city was subdivided into 487 regions, each with an area of 1-mi². A total of 389 bombs hit the combined area of 487 regions. The Poisson distribution applies because we are dealing with the occurrences of an event (bomb hits) over some interval (a region with area of 1-mi².

Find the mean number of hits per region:
mean =

Find the standard deviation of hits per region:
standard deviation =

If a region is randomly selected, find the probability that it was hit exactly twice.
(Report answer accurate to 4 decimal places.)
P(X=2)=P(X=2)=

Based on the probability found above, how many of the 487 regions are expected to be hit exactly twice?
(Round answer to a whole number.)
ans =

If a region is randomly selected, find the probability that it was hit at most twice.
(Report answer accurate to 4 decimal places.)
P(X≤2)=P(X≤2)=

6.2.38 Big Babies: The Centers for Disease Control and Prevention reports that 25% of baby boys 6-8 months old in the United States weigh more than 20 pounds. A sample of 16 babies is studied. (Use Minitab where applicable.)

a.         What is the probability that exactly 5 of them weigh more than 20 pounds?

b.         What is the probability that more than 6 weigh more than 20 pounds?

c.         What is the probability that fewer than 3 weigh more than 20 pounds?

d.         Would it be unusual if more than 8 of them weigh more than 20 pounds?

e.         What is the mean number who weigh more than 20 pounds in a sample of 16 babies aged 6-8 months?

f.          What is the standard deviation of the number who weigh more than 20 pounds in a sample of 16 babies ages 6-8 months?

(1) According to the American Lung Association, 90% of adult smokers started smoking before turning
21 years old. Ten smokers 21 years old or older were randomly selected, and the number of smokers
who started smoking before 21 is recorded.
(a) State the distribution of the random variable of number of smoker of these 10 who started
smoking before age 21 and its two parameters.
(b) Find the probability that exactly 8 of them started smoking before 21 years of age. Do not
use statistical features of your calculator.
(c) Find the probability that fewer than 8 of them started smoking before 21 years of age.
(d) Find the probability that between 7 and 9 of them, inclusively, started smoking before 21 years
of age.
(e) Compute and interpret the mean of this random variable.
(f) Compute the standard deviation of this random variable.

In analyzing hits by bombs in a past war, a city was subdivided into 552 regions, each with an area of 0.25-km². A total of 447 bombs hit the combined area of 552 regions. The Poisson distribution applies because we are dealing with the occurrences of an event (bomb hits) over some interval (a region with area of 0.25-km².

Find the mean number of hits per region:
mean =

Find the standard deviation of hits per region:
standard deviation =

If a region is randomly selected, find the probability that it was hit exactly twice.
(Report answer accurate to 4 decimal places.)
P(X=2)=P(X=2)=

Based on the probability found above, how many of the 552 regions are expected to be hit exactly twice?
(Round answer to a whole number.)
ans =

If a region is randomly selected, find the probability that it was hit at most twice.
(Report answer accurate to 4 decimal places.)
P(X≤2)=P(X≤2)=

A) Lance the Wizard has been informed that tomorrow there will be a 50% chance of encountering the evil Myrmidons and a 30% chance of meeting up with the dreadful Balrog. Moreover, Hugo the Elf has predicted that there is a 10% chance of encountering both tomorrow. What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog?

B)The astrology software package, Turbo Kismet,† works by first generating random number sequences and then interpreting them numerologically. When I ran it yesterday, it informed me that there was a 1/3 probability that I would meet a tall dark stranger this month, a 2/3 probability that I would travel this month, and a 1/9 probability that I would meet a tall dark stranger and also travel this month. What is the probability that I will either meet a tall dark stranger or that I will travel this month? HINT [See Example 4.] (Enter your probability as a fraction.)