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7.84 Random Variables and Discrete Probability Distributions

Given a binomial random variable with n = 10 and p = .3, use the formula to find the
following probabilities.
a. P(X = 3)
b. P(X = 5)
c. P(X = 8)
7.97 Random Variables and Discrete Probability Distributions

In the United States, voters who are neither Democrat 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.
8.35 Continuous Probability Distributions
 Xis normally distributed with mean 250 and standard deviation 40. What value of X does
only the top 15% exceed?
8.42 Continuous Probability Distributions

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.
13.5 Inference about comparing two populations
In random samples of 25 from each of two normal populations, we found the following statistics:
x̄1 = 524
s1 = 129
x̄2 = 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 samples of size 100.

e. Discuss the effects of increasing the sample size.
13.8 Inference about comparing two populations
x̄1 = 412
s1 = 128
x̄2 = 405
s2 = 54
 a. Can we infer at the 5% significance level that μ1 is greater than μ2?
 b. Repeat part (a) decreasing the standard deviations to s1 = 31 and s2 = 16.
n1 = 150
n2 = 150
 c. Describe what happens when the sample standard deviations get smaller.
 d. Repeat part (a) with samples of size 20.
 e. Discuss the effects of decreasing the sample size.
 f. Repeat part (a) changing the mean of sample 1 to x̄1 = 409
 g. Discuss the effect of decreasing x̄1.
15.60 Chi-Squared Tests
 A random sample of 50 observations yielded the following frequencies for the
standardized intervals:
Interval
Z ≤ −1
Frequency
6
−1 < Z ≤ 0
27
0<Z≤1
14
Z>1
3
Can we infer that the data are not normal? (Use α = .10.)
15.68 Chi-Squared Tests. Set up a contingency table in Excel to answer the following question
Suppose that the personnel department in Exercise 15.42 continued its investigation by
categorizing absentees according to the shift on which they worked, as shown in the
accompanying table. Is there sufficient evidence at the 10% significance level of a relationship
between the days on which employees are absent and the shift on which the employees work?
Day of the Week
Day
Monday
52
Tuesday
28
Wednesday
37
Thursday
31
Thursday
33
Evening
35
34
34
37
41