Stats Exam 3

A professor divided the students in her business class into three​ groups: those who have never taken a statistics​ class, those who have taken only one semester of a statistics​ class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. If​ 35% of the students have never taken a statistics​ class, 25% have taken only one semester of a statistics​ class, and the rest have taken two or more semesters of​ statistics, what is the probability that neither of the first two groupmates you meet has studied any​ statistics? Round to three decimal places.

0.123

College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. toppings freshman sophomore junior senior cheese 16 16 26 29 meat 25 29 16 16 veggie 16 16 25 29 Given that a​ student's favorite topping is​ meat, what is the probability that the student is a​ junior? Round to three decimal places.

0.186

College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. toppings freshman sophomore junior senior cheese 16 16 26 29 meat 25 29 16 16 veggie 16 16 25 29 Find​ P(favorite topping is meat​ | student is​ junior). Round to three decimal places.

0.239

A manufacturing process has a​ 70% yield, meaning that​ 70% of the products are acceptable and​ 30% are defective. If three of the products are randomly​ selected, find the probability that all of them are acceptable.

0.343

A professor divided the students in her business class into three​ groups: those who have never taken a statistics​ class, those who have taken only one semester of a statistics​ class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. If​ 55% of the students have never taken a statistics​ class, 25% have taken only one semester of a statistics​ class, and the rest have taken two or more semesters of​ statistics, what is the probability that the first groupmate you meet has studied some​ statistics?

0.45

In a blood testing​ procedure, blood samples from 5 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is​ 0.12, what is the probability that the mixture will test​ positive? Round to three decimal places.

0.472

In one​ city, 47.5% of adults are​ female, 10.2% of adults are​ left-handed, and​ 4.8% are females who are left handed. For an adult selected at random from the​ city, let Fequals=event the person is female Lequals=event the person is​ left-handed. Find​ P(F or​ L). Round to three decimal places.

0.529

The number of hours per week that high school seniors spend on homework is normally​ distributed, with a mean of 10 hours and a standard deviation of 3 hours. 60 students are chosen at random. Let represent the mean number of hours spent on homework for this group. Find the probability that is between 9.8 and 10.4. Round to three decimal places.

0.547

A survey of senior citizens at a​ doctor's office shows that​ 40% take blood​ pressure-lowering medication,​ 47% take​ cholesterol-lowering medication, and​ 13% take both medications. What is the probability that a senior citizen takes either blood​ pressure-lowering or​ cholesterol-lowering medication?

0.74

A professor divided the students in her business class into three​ groups: those who have never taken a statistics​ class, those who have taken only one semester of a statistics​ class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. If​ 10% of the students have never taken a statistics​ class, 35% have taken only one semester of a statistics​ class, and the rest have taken two or more semesters of​ statistics, what is the probability that both of the first two groupmates you meet have studied at least one semester of​ statistics?

0.81

Based on a sample of 30 randomly selected​ years, a​ 90% confidence interval for the mean annual precipitation in one city is from 48.7 inches to 51.3 inches. Find the margin of error.

1.3 inches

In a Stats​ class, 57% of students eat breakfast in the morning and​ 80% of students floss their teeth. ​Forty-six percent of students eat breakfast and also floss their teeth. What is the probability that a student from this class eats breakfast but does NOT​ floss?

11%

Assume that​ 15% of students at a university wear contact lenses. We randomly pick 200 students. What is the mean of the proportion of students in this group who may wear contact​ lenses?

15

A survey found that​ 79% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of error for this survey if we want​ 90% confidence in our estimate of the percent of American adults who approve of cloning endangered animals.

2.09

Assume that​ 10% of students at a university wear contact lenses. We randomly pick 200 students. What is the standard deviation of the proportion of students in this group who may wear contact​ lenses? Round to two decimal places.

2.12%

Using​ t-tables, software, or a​ calculator, estimate the critical value of t for a​ 99% confidence interval with df=24. Round to three decimal places as needed.

2.797

Based on a sample of size​ 49, a​ 95% confidence interval for the mean score of all​ students, muμ​, on an aptitude test is from 59.2 to 64.8. Find the margin of error.

2.8

A​ university's administrator proposes to do an analysis of the proportion of graduates who have not found employment in their major field one year after graduation. In previous​ years, the percentage averaged​ 15%. He wants the margin of error to be within​ 5% at a​ 99% confidence level. What sample size will​ suffice? Round to the nearest integer.

339

Political analysts estimate the probability that Candidate A will run for president in 2016 is​ 45%, and the probability that Candidate B will run is​ 20%. If their political decisions are​ independent, then what is the probability that only Candidate A runs for​ president?

36%

Based on past​ experience, a bank believes that​ 4% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans. What is the mean of the proportion of clients in this group who may not make timely​ payments?

4%

In a survey of 300 T.V.​ viewers, 40% said they watch network news programs. Find the margin of error for this survey if we want​ 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs. Round to two decimal places.

5.54%

In a Stats​ class, 57% of students eat breakfast in the morning and​ 80% of students floss their teeth. ​Forty-six percent of students eat breakfast and also floss their teeth. What is the probability that a student from this class eats breakfast or​ flosses?

91%

Data in 1980 showed that about​ 40% of the adult population had never smoked cigarettes. In​ 2004, a national health survey interviewed a random sample of 2000 adults and found that​ 50% had never been smokers. Create a​ 95% confidence interval for the proportion of adults​ (in 2004) who had never been smokers. Round to the nearest tenth.

Based on the​ data, we are​ 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between​ 47.8% and​ 52.2%.

We have calculated a​ 95% confidence interval and would prefer for our next confidence interval to have a smaller margin of error without losing any confidence. In order to do​ this, which of the following statements is​ TRUE? I. we can change the​ z- value to a smaller number. II. we can take a larger sample. III. we can take a smaller sample.

II only

Of 346 items​ tested, 12 are found to be defective. Construct a​ 98% confidence interval for the percentage of all such items that are defective. Round to two decimal places.

​(1.18%, 5.76%)

The amounts​ (in ounces) of juice in eight randomly selected juice bottles are​ 15.0, 15.9,​ 15.8, 15.7,​ 15.4, 15.2,​ 15.2, and 15.3. Construct a​ 98% confidence interval for the mean amount of juice in all such bottles. Round to two decimal places as needed.

​(15.09, 15.78)

n=​12, x overbar=​28.0, s=5.7. Find a​99% confidence interval for the mean. Round to two decimal places as needed.

​(22.89, 33.11)

When 346 college students are randomly selected and​ surveyed, it is found that 121 own a car. Construct a​ 99% confidence interval for the percentage of all college students who own a car. Round to one decimal place.

​(28.4%, 41.6%)

n=​10, x overbar=​13.0, s=4.5. Find a​95% confidence interval for the mean. Round to two decimal places as needed.

​(9.78, 16.22)

A certain population is bimodal. We want to estimate its​ mean, so we will collect a sample. Which should be TRUE if we use a large sample rather than a small​ one? I. The distribution of our sample data will be more clearly bimodal. II. The sampling distribution of the sample means will be approximately normal. III. The variability of the sample means will be smaller.

​I, II, and III