Statistics and Probability Answers

A manufacturer claims that his light bulbs have an average life time of 1500 hours. A purchaser decides to check this claim and finds that for six bulbs the lifetimes are 1472,1486,1401,1350,1610,1590, hours. Does this evidence support the manufacturer’s claim? Assume that the lifetimes of the light bulbs are normally distributed.

A continuous random variable has a density function f (x) = 2 (5-x)/5, where 2<x<3. Calculate the probability

A car wholesaler estimates the quantity of new cars retailed that have been returned back a many
number of times for the rectification of defects during the warranty. The results are given in the
following table. Show complete working.

Number of cars
returns back 0 1 2 3 4

Probability 0.25 0.34 0.22 0.07 0.03

a. Compute the mean of the number of cars returns for rectifications for defects during the
warranty time.

b. Calculate the variance of the number of cars returns for rectifications for defects during
the warranty time.

A car wholesaler estimates the quantity of new cars retailed that have been returned back a many
number of times for the rectification of defects during the warranty. The results are given in the
following table. Show complete working.
Number of cars
returns back
0 1 2 3 4
Probability 0.25 0.34 0.22 0.07 0.03
a. Compute the mean of the number of cars returns for rectifications for defects during the
warranty time.
b. Calculate the variance of the number of cars returns for rectifications for defects during
the warranty time.

A continuous random variable has a density function�(�) = 2(5 – x)
5
, where 2<x<3. Calculate
the following probability correct up to 3 decimal places, and make the graph for part (a) only in
Answer sheet:
P (x < 2.5)
P (x > 2.2)
P (2.1 ≤ � ≤ 2.7)

Transit Railroads is interested in the relationship between travel distance and ticket class
purchased. A random sample of 200 passengers is taken. Table 3 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must
travel.

Traveling
Distance
Third class Second class First class Total
1-100 miles 21 14 6 41
101-200 miles 18 16 8 42
201-300 miles 16 17 15 48
301-400 miles 12 14 21 47
401-500 miles 6 6 10 22
Total 73 67 60 200

Table 3

a. State the hypotheses.
b. State the degree of freedom
c. How many passengers are expected to travel between 201 and 300 miles and
purchase second-class tickets?
d. How many passengers are expected to travel between 401 and 500 miles and
purchase first-class tickets?
e. What is the test statistic?
f. What is the p-value?
g. What can you conclude at the 5% level of significance?

(5.2.28) Based on a​ poll, among adults who regret getting​ tattoos, ​19% say that they were too young when they got their tattoos. Assume that 5 adults who regret getting tattoos are randomly​ selected, and find the indicated probability.
A.Find the probability that none of the selected adults say that they were too young to get tattoos

(5.2.27) Based on a​ poll, 60​% of adults believe in reincarnation. Assume that 6 adults are randomly​ selected, and find the indicated probability.
A. The probability that exactly 5 of the 6 adults believe in reincarnation is ?

Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at
random and asked about the number of hours a week they work. The results are shown in Table 4
20–30 30–40 40–50 50–60
Private
Practice
16 40 38 6
Hospital 8 44 59 39
Table 4
a. State the null and alternative hypotheses.
b. State the degree of freedom.
c. What is the test statistic?
d. What is the p-value?
e. What can you conclude at the 5% significance level?

Zane is interested in the proportion of people who recycle each of three distinct products: paper, plastic, and electronics. He wants to test the hypothesis that the proportion of people recycling each type of product differs by age group: 12-18 years old, 19-30 years old, 31-40 years old, and over 40 years old. Suppose he found a sample χ2 = 16.83.
a. How many d.f are used? Approximate the P-value and conclude the test at the 1% level of significance. Does it appear that the proportion of people who recycle each of the specified products differ by age group? Explain.
b. From this study, can Zane identify how the different age groups differ regarding the proportion of those recycling the specified products? Explain.