**QUESTION**

Show enough of your work so that I will be able to tell how you arrived at your answers.

- Consider the probability distribution below.

__x P(x) __

10 0.1

20 0.2

30 0.3

40 0.3

50 0.1

- Calculate the probability that a randomly selected value of X will be less than 36.
- Calculate μ = E(X).
- Calculate σ
^{2 }= σ^{2}(X).

2. Given that X has a binomial distribution with n = 10 and p = 0.30, find the following:

- the mean, μ
- the variance, σ
^{2}. - P(X = 2)

- Given that X has a Poisson distribution for which the average rate of occurrences is 0.04 per day and the length of the interval is 12 days, find the following:
- the mean of X
- the variance of X

- Assume that Y has an exponential distribution with λ = 4 per meter. Find . . .
- E(Y)
- σ
^{2}(Y)

- Suppose customers contact a health agency’s on-line help desk randomly and independently at an average rate of 6 per hour. Find . . .

- the average time between the beginning of one contact and the beginning of the next contact.
- the average number of contacts in a 12-minute period.
- the probability that there will be exactly two contacts between 4:00 and 4:12.
- the probability that the length of time from now until the next contact will be more than 15 minutes.

6. Find each of the following normal probabilities. Z has a standard normal distribution.

- P(Z < 1.86)
- P(-0.73 < Z < 1.19)

7.The time it takes an experienced installer to install a device in a customer’s home has a normal distribution with a mean of 52 minutes and a variance of 100 minutes^{2}. The management wants to know the probability that an installation job will take more than one hour. Calculate this probability.

**ANSWER**

1.a)

1.b)

2.a)

2.b)

2.c)

3.a)

3.b)

4.a,b)

5.a)

5.b)

5.c)

5.d)

6.a)

6.b)

7)

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