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Exercise 1 Given a binomial random...

Exercise 1

Given a binomial random variable with n=10 and p=.3, Use the formla to find the following probabilities.

a. P(X = 3)

b. P(X = 5)

c. P(X = 8)

Exercise 2

In the United States, voters who are neither Democrate nor Republican are called Independents. It is believed that 10% of all voters are Independents. A survey asked 25 people to identify themselves as Democrat, Republican or Independent.

a. What is the probability that none of the people are Independents?

b. What is the probability that fewer than five people are Independents?

c. What is the probability that more than two people are Independents?

Exercise 3

X is normally distributed with mean 250 and standard deviation 40. What value of X does only the top 15% exceed?

Exercise 4

Travelbyus is an Internet-based travel agency wherein customers can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.

a. What is the probability of getting more than 12,000 hits?

b. What is the probability of getting fewer than 9,000 hits?

Exercise 5

In random samples of 25 from each of two normal populations, we found the following statistics:

X1 = 524 S1 = 129

X2 = 469 S2 = 141

a. Estimate the difference between the two population means with 95% confidence.

b. Repeat part (a) increasing the standard deviations to S1 = 255 and S2 = 260.

c. Describe what happens when the sample standard deviations get larger.

d. Repeat part (a) with sample of size 100.

e. Discuss the effects of increasing the sample size.

Exercise 6

Random sampling from two normal populations produced the following results:

X1 = 412 S1 = 128 n1 = 150

X2 = 450 S2 = 54 n2 = 150

a. Can we infer at the 5% significance level that u1 is greater than u2?

b. Repeat part (a) decreasing the standard deviation to S1 = 31 and S2 =s 16.

c. Describe what happens when the sample standard deviation get smaller.

d. Repeat part (a) with sample size 20.

e. Discuss the effects of decreasing the sample size.

f. Repeat part (a) changing the mean of sample 1 to x = 409.

g. Discuss the effect of decreasing X1.

Exercise 7

A random sample of 50 observations yielded the following frequencies for the standardized intervals:

Interval Frequency

Z < -1 6

-1< Z< 0 27

0< Z 1 3

Exercise 8

Day of the week Monday Tuesday Wednesday Thursday Friday

Number absent 87 62 71 68 74

Suppose that the personnel department is Exercise 15.55 continued its investigation by categorizing absentees according to the shift on which they worked, as shown in the

Given a binomial random variable with n=10 and p=.3, Use the formla to find the following probabilities.

a. P(X = 3)

b. P(X = 5)

c. P(X = 8)

Exercise 2

In the United States, voters who are neither Democrate nor Republican are called Independents. It is believed that 10% of all voters are Independents. A survey asked 25 people to identify themselves as Democrat, Republican or Independent.

a. What is the probability that none of the people are Independents?

b. What is the probability that fewer than five people are Independents?

c. What is the probability that more than two people are Independents?

Exercise 3

X is normally distributed with mean 250 and standard deviation 40. What value of X does only the top 15% exceed?

Exercise 4

Travelbyus is an Internet-based travel agency wherein customers can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.

a. What is the probability of getting more than 12,000 hits?

b. What is the probability of getting fewer than 9,000 hits?

Exercise 5

In random samples of 25 from each of two normal populations, we found the following statistics:

X1 = 524 S1 = 129

X2 = 469 S2 = 141

a. Estimate the difference between the two population means with 95% confidence.

b. Repeat part (a) increasing the standard deviations to S1 = 255 and S2 = 260.

c. Describe what happens when the sample standard deviations get larger.

d. Repeat part (a) with sample of size 100.

e. Discuss the effects of increasing the sample size.

Exercise 6

Random sampling from two normal populations produced the following results:

X1 = 412 S1 = 128 n1 = 150

X2 = 450 S2 = 54 n2 = 150

a. Can we infer at the 5% significance level that u1 is greater than u2?

b. Repeat part (a) decreasing the standard deviation to S1 = 31 and S2 =s 16.

c. Describe what happens when the sample standard deviation get smaller.

d. Repeat part (a) with sample size 20.

e. Discuss the effects of decreasing the sample size.

f. Repeat part (a) changing the mean of sample 1 to x = 409.

g. Discuss the effect of decreasing X1.

Exercise 7

A random sample of 50 observations yielded the following frequencies for the standardized intervals:

Interval Frequency

Z < -1 6

-1< Z< 0 27

0< Z 1 3

Exercise 8

Day of the week Monday Tuesday Wednesday Thursday Friday

Number absent 87 62 71 68 74

Suppose that the personnel department is Exercise 15.55 continued its investigation by categorizing absentees according to the shift on which they worked, as shown in the

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