*label*Mathematics

### Question Description

1. The following is suppose to represent probability distribution table. What is the missing value?

X

P(X)

3

0.4

5

0.5

9

?

2. Find the expected value of X using the table below.

X

P(X)

0

0.4

1

0.3

─1

0.3

3. If the standard deviation of a random variable is 5,what is its variance?

4. Any normal distribution is

continuous

discrete

5.

some are discrete, some are continuous

a binomial distribution

6.

is Poisson distribution

5. Let X be a binomial random variable with number of trials 100 and expected value 20. What is the probability of success of X?

6. There are 17 blue, 5 green, and 3 red balls in a jar. We randomly select a ball and return it back to the jar. We repeat it 8 times. To find the probability of the event that every time we get a green ball we need to use the following distribution:

binomial with number of trials 8 and probability of success 0.2

binomial with number of trials 25 and probability of success 0.5

binomial with number of trials 5 and probability of success 0.2

binomial with number of trials 8 and probability of success 0.8

binomial with number of trials 8 and probability of success 1/3

Poisson Distribution with average 5

Poisson Distribution with average 8

binomial with number of trials 25 and probability of success 0.2

7. The average number of homes with 3 or more bedrooms sold by Acme Reality is 14 homes per week. To find the probability that exactly 3 such homes will be sold tomorrow we need to use the following distribution:

Poisson distribution with mean 2

Poisson distribution with mean 14

Poisson distribution with mean 7

Poisson distribution with mean 3

Binomial with number of trials 7 and probability of success 2/7

Binomial with number of trials 2 and probability of success 2/7

Binomial with number of trials 7 and probability of success 1/7

Standard normal distribution

8. A random variable X assumes values 1,2,3,..., 8,9,and 10, each with the same probability, namely the probability 0.1. Find the probability of X getting at least 3.

9. A random variable X assumes values 1,2,3,..., 8,9,10, each with the same probability, namely the probability 0.1. Find the probability of X getting no more than 4.

10. A card is drawn, with replacement, from a regular deck of cards 16 times. Let random variable X represent number of clubs among those 16 cards selected (there are 13 clubs in every deck; there are 52 cards in a deck). Find the variance of X,

11. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last less than 7 months.Round to the nearest thousandth.

12. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months.Find the probability that an instrument produced by this machine will last between 7 and 12 months. Round to the nearest thousandth.

13. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find how long an instrument that separates the bottom 83.398% will last? Round to the nearest hundredth.

14. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. What is the probability that the average number of months that these 100 instruments will last is greater than 12.2 months? Round to the nearest thousandth.

15. A die is rolled 360 times. If you want to use normal approximation to find the probability that the number of 4 was rolled at least 100 times,what is the mean of the normal distribution that you would use in this case.

16. A die is rolled 180 times. If you want to use normal approximation to find the probability that the number of 4 was rolled at least 20 times,what is the standard deviation of the normal distribution that you would use in this case

17. A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled less than 100 times. You need to find the probability that X<100. Explain how you would use continuity correction in this case.

18. A die is rolled 360 times. Let say that you want to use normal approximation to find the probability that the number of 4 was rolled exactly 100 times. You need to find the probability that X=100. Explain how you would use continuity correction in this case.

19. What is the name of the theorem that states that the sampling distribution of the sample mean is approximately normal when the sample is large?

20. Determine whether the following random variables have a binomial distribution:

A) Ten students are chosen from a statistics class (with replacement) of 400 students. Let X be the number of students who passed the class.

B) A die is tossed three times. Let X be the sum of the three numbers obtained.

C) A coin is tossed until a head appears. Let X be the number of tosses.

only A is a binomial distribution

only B is a binomial distribution

only C is a binomial distribution

only A and B is a binomial distribution

only A and C is a binomial distribution

only B and C is a binomial distribution

all A, B, and C are binomial distributions

none is a binomial

## Tutor Answer

I have noted. Answers will still be as below.1.X p(x)9 0.12.03.254.continuous5.0.26.binomial with number of trials 8 and probability of success 0.27.Poisson distribution with mean 148.0.89.0.410.3

11.0.00612.0.49413.13.9414.0.15915.60

16.517.Correct...

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