# The population

The population mean annual salary for environmental compliance specialists is about \$63,000. 63,000. A random sample of 34 34 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than \$60,000. Assume standard deviation is 6,100

The mean height of women in a country (ages 20-29) is 63.9 inches. A random sample of 50 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume σ= 2.51.
The probability that the mean height for the sample is greater than 65 inches
A manufacturer claims that the life span of its tires is 47,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 46,900 miles. Assume σ=800. (a) Assuming the manufacturer’s claim is correct, what is the probability that the mean of the sample is 46,900 or less.
z = (xbar – µ) / (σ / √n) = (46900 – 47000) / (800 / √100) = -1.25
A population has a mean μ=88 and a standard deviation σ=32. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=64.
use the normal distribution of SAT critical reading scores for which the mean is
508 and the standard deviation is 119.
Assume the variable x is normally distributed.
a) What percent of the SAT verbal scores are less than
600?
(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than
525?
The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.4 fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly selected.
(a) Find the probability that the drink is less than 12.2 fluid ounces.
(b) Find the probability that the drink is between 11.9 and 12.2 fluid ounces.
(c) Find the probability that the drink is more than 12.8 fluid ounces.
In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.2 inches and a standard deviation of 3.0 inches. A study participant is randomly selected.
The probability that the study participant selected at random is less than 67 inches tall is
Find the probability that a study participant has a height that is between 67 and 70 inches.
Find the probability that a study participant has a height that is more than 70 inches.
Assume the Poisson distribution applies. Use the given mean to find the indicated probability.Find P(4) when μ=5.
In a sample of 1200 U.S. adults, 204 dine out at a resaurant more than once per week.
Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete parts (a) through (d)(a) Find the probability that both adults dine out more than once per week.
(b) Find the probability that neither adult dines out more than once per week.
(c) Find the probability that at least one of the two adults dines out more than once per week.
The probability that a randomly selected adult dines out more than once a week is p = x/n
A state lottery randomly chooses 8 balls numbered from 1 through 35
without replacement. You choose 8 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x.
The table below shows the results of a survey that asked 1060 adults from a certain country if they would support a change in their country’s flag. A person is selected at random. Complete parts (a) through (d).Support Oppose Unsure Total
Males 162 330 8 500
Females 243 299 18 560
Total 405 629 26 1060(a) Find the probability that the person opposed the change or is female.
(b) Find the probability that the person supports the change or is male.
(c) Find the probability that the person is not unsure or is female.
Fifty-five percent of households say they would feel secure if they had \$50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had \$50,000 in savings. Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five.
A company that makes cartons finds that the probability of producing a carton with a puncture is 0.05,the probability that a carton has a smashed corner is 0.1, and the probability that a carton has a puncture and has a smashed corner is 0.005.
If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed corner.
The table below shows the results of a survey in which 141
men and 144 women workers ages 25 to 64 were asked if they have at least one month’s income set aside for emergencies. Complete parts (a) through (d).Men Women Total
Less than one month’s income 65 83 148
One month’s income or more 76 61 137
Total 141 144 285(a) Find the probability that a randomly selected worker has one month’s income or more set aside for emergencies.
(b) (b) Given that a randomly selected worker is a male, find the probability that the worker has less than one month’s income.
(c) Given that a randomly selected worker has one month’s income or more, find the probability that the worker is a female.
(d) Are the events “having less than one month’s income saved” and “being male” independent or dependent?
use the frequency distribution to the right, which shows the number of voters (in millions) according to age, to find the probability that a voter chosen at random is in the given age range.
Ages of voters Frequency
18 to 20 5.1
21 to 24 8.4
25 to 34 24.6
35 to 44 25.4
45 to 64 57.6
65 and over 26.4Not between 18-20 years old: the probability is