exam 2 stats (5-7)

A brand of water softener salt comes in packages marked "net weight 40 lbs". The company that packages the salt claims that the bags contain an average of 40 lb. of salt and that the standard deviation of the weights is 2.0 lb. assume that the weights are normally distributed. For samples of size 100, find the standard deviation of the distribution of all possible sample mean weights (i.e., find the standard error of all possible sample mean weights).

.20

Estimate the probability of the event. A frequency distribution on employment information from Alpha Corporation follows.. Find the probability that an employee has been with the company between 16 and 25 years. yrs employed; no. of employ 1-5; 5 6-10;20 11-15;25 16-20;10 21-25;5 26-30;3

.221

Estimate the probability of the event. A frequency distribution on employment information from Alpha Corporation follows.. Find the probability that an employee has been with the company 10 years or less. yrs employed; no. of employees 1-5;5 6-10;20 11-15;25 16-20; 10 21-25;5 26-30;3

.368.368

The distribution of B.A. degrees conferred by a local college is listed below, by major. Major Frequency English 2073 Mathematics 2164 Chemistry 318 Physics 856 Liberal Arts 1358 Business 1676 Engineering 868 9313 What is the probability that a randomly selected degree is in English or Mathematics (assume no double majors)?

.455

Find the indicated probability by using the general addition rule. In one city, 50.8% of adults are female, 9.6% of adults are left-handed, and 5.1% are left-handed females. For an adult selected at random from the city, let F = event the person is female L = event the person is left-handed. Find P(F or L). Round approximations to three decimal places.

.553

Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 2 pounds per square inch. What is the probability that a sample of 16 such bags will have an average breaking strength less than 6 pounds per square inch? (Choose the closest answer. Answers are rounded to the fourth decimal place).

.9772

Z is the standard normal random variable with mean 0 and standard deviation 1. What is P(Z > 6)? (Choose the closest answer):

0

Monthly cell phone bill is assumed to follow a normal distribution with a mean of $47 and standard deviation $8. What is the probability that a randomly selected phone bill will be more than $67?

0.0062

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

0.0166

The average weight of a certain part manufactured by a company is 15 kg with a standard deviation of 0.6 kg. If 36 of these parts are randomly selected, what is the probability the average weight will be at least 15.2 kg?

0.0228

Suppose that D is a random variable. Given that P(D > 4.4) = 0.95, find P(D 4.4).

0.05

Monthly cell phone bill is assumed to follow a normal distribution with a mean of $47 and standard deviation $8. What is the probability that a randomly selected phone bill will be more than $59?

0.0668

A brand of water softener salt comes in packages marked "net weight 40 lbs". The company that packages the salt claims that the bags contain an average of 40 lb. of salt and that the standard deviation of the weights is 0.6 lb. assume that the weights are normally distributed. For samples of size 36, find the standard deviation of the distribution of all possible sample mean weights (i.e., find the standard error of all possible sample mean weights).

0.1

Suppose out of a population of 400 people, 50 have received at least one speeding ticket in the last year. If one person out of this population is selected at random, what is the probability that person has received at least one speeding ticket in the last year?

0.125

Suppose out of a population of 1000 people, it is believed that 800 have a genetic disorder. If one person out of the population was randomly selected, what is the probability that person will not have the genetic disorder?

0.20

Estimate the probability of the event. In a certain class of students, there are 10 boys from Wilmette, 5 girls from Kenilworth, 10 girls from Wilmette, 7 boys from Glencoe, 5 boys from Kenilworth and 6 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?

0.233

Use the following probability distribution to determine P(6 < X 8). All outcomes are mutually exclusive. x: P(X=x) 5: 0.05 6: 0.05 7: 0.20 8: 0.15 9: 0.15 10: 0.10 11: 0.30

0.35

Estimate the probability of the event. yrs employed; # of employees 1-5;5 6-10;20 11-15;25 16-20;10 21-25; 5 26-30; 3 A frequency distribution on employment information from Alpha Corporation follows.. Find the probability that an employee has been with the company 10 years or less.

0.368

Find the indicated probability or percentage for the normally distributed variable. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220.

0.3811

Find the indicated probability or percentage for the normally distributed variable. The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

0.4013

Find the indicated probability or percentage for the normally distributed variable. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

0.4332

The distribution of B.A. degrees conferred by a local college is listed below, by major. Major Frequency English 2073 Mathematics 2164 Chemistry 318 Physics 856 Liberal Arts 1358 Business 1676 Engineering 868 9313 What is the probability that a randomly selected degree is in English or Mathematics (assume no double majors)?

0.455

Find the indicated probability by using the general addition rule. In one city, 50.8% of adults are female, 9.6% of adults are left-handed, and 5.1% are left-handed females. For an adult selected at random from the city, let F = event the person is female L = event the person is left-handed. Find P(F or L). Round approximations to three decimal places.

0.553

Use a table of areas to obtain the shaded area under the standard normal curve.

0.6424

From a given population, it is known that 68% are female, 20% are smokers, and 16% are females who smoke. What is the probability that a randomly selected person from this population will be female or a smoker?

0.72

Use a table of areas to obtain the shaded area under the standard normal curve. (-1.17 to 1.17)

0.7580

From a given population, it is known that 58% are female, 35% are smokers, and 16% are females who smoke. What is the probability that a randomly selected person from this population will be female or a smoker?

0.77

Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 2 pounds per square inch. What is the probability that a sample of 16 such bags will have an average breaking strength less than 6 pounds per square inch? (Choose the closest answer. Answers are rounded to the fourth decimal place).

0.9772

Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1 pound per square inch. What is the probability that a sample of 9 such bags will have an average breaking strength less than 6 pounds per square inch? (Choose the closest answer. Answers are rounded to the fourth decimal place).

0.9987

Monthly cell phone bill is assumed to follow a normal distribution with a mean of $47 and standard deviation $8. Suppose 4 cell phone bills are randomly selected. What is the probability that the average of these 4 bills will be less than $63?

1

Z is the standard normal random variable with mean 0 and standard deviation 1. What is P(Z < 6)? (Choose the closest answer):

1

Suppose we have an experiment and the sample space is S = {100, 200, 300, 400, 500}. Further suppose we are interested in the event of getting a 100, 200, and 300 (that is A = {100, 200, 300} and the event of getting 100, 300, or 500 (that is B = {100, 300, 500}). All outcomes in the sample space are equally likely to occur. In this situation, what is P(A and B)?

2/5 or 0.40

The mean annual salary for all public classroom teachers is assumed to be $49,000. The standard deviation of annual salary for all public classroom teachers is assumed to be $9,200. A random sample of 300 public classroom teachers is selected from which it is found an average salary of $45,000 with a standard deviation of $10,000. In this given scenario, which value is the sample standard deviation, s?

$10,000

The mean annual salary for all public classroom teachers is assumed to be $49,000. The standard deviation of annual salary for all public classroom teachers is assumed to be $9,200. A random sample of 300 public classroom teachers is selected from which it is found an average salary of $45,000 with a standard deviation of $10,000. In this given scenario, which value is the sample mean, x-bar?

$45,000

Use a table of areas for the standard normal curve to find the required z-score. Find the z-score having area 0.86 to its right under the standard normal curve; that is, find z0.86.

-1.08

Use the standard normal curve find the value of z when the area to its left is 0.04

-1.75

Provide an appropriate response. What generally happens to the sampling error as the sample size is increased?

It gets smaller.

It is known that two events, A, B, are mutually exclusive. Which of the following is true?

P (A and B) = 0

Suppose we have an experiment and the sample space is S = {100, 200, 300, 400, 500}. Further suppose we are interested in the event of getting a 100 or 200 (that is A = {100, 200} and the event of getting 100, 300, or 500 (that is B = {100, 300, 500}). In this situation, what outcomes are in the event A and B?

{100}

According to an article, the average age of a self-employed individual is 46.6 years with a standard deviation of 10.8 years. For a sample of size 100, what is the standard deviation of the sample mean, xbar (i.e., what is the standard error for a sample of size 100)?

1.08

Use a table of areas for the standard normal curve to find the required z-score. Find the z-score for having area 0.09 to its right under the standard normal curve, that is, find z0.09

1.34

From the standard normal table, find the value of z that has an area of 0.05 to its right.

1.645

Suppose we have an experiment and the sample space is S = {100, 200, 300, 400, 500}. Further suppose we are interested in the event of getting a 100 or 200 (that is A = {100, 200} and the event of getting 100, 300, or 500 (that is B = {100, 300, 500}). In this situation, what outcomes are in the event A and B?

100

A random variable X follows a normal distribution with a mean of 10 and standard deviation of 3. A standardized value of X was found to be Z = 2. The value of X is then

16

A random variable X follows a normal distribution with a mean of 10 and standard deviation of 3. A standardized value of X was found to be Z = 2.5. The value of X is then

17.5

A random variable X follows a normal distribution with a mean of 10 and standard deviation of 3. A standardized value of X was found to be Z = 3. The value of X is then

19

Determine the number of outcomes that comprise the specified event. The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2196 21-25 2057 26-30 1179 31-35 832 Over 35 223 A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is between 21 and 35 inclusive B = event the student is 26 or over Determine the number of outcomes that comprise the event (A and B).

2011

Find the indicated probability or percentage for the normally distributed variable. The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation $150. What percentage of trainees earn less than $900 a month?

9.18%

True or false, the standard deviation of a normally distributed variable can be any real number.

False

Suppose a study is being conducted involving statistics about naturalized persons in the U.S. Suppose a naturalized person is chosen at random. Let A = event the person is younger than 20 years old. What is the complement of this event?

The chosen person is 20 years old or older.

In order to apply the Central Limit Theorem to a particular problem, the population of the individual observations, X, must be normally distributed.

false

Provide an appropriate response. The mean height for a population is 65 inches and the standard deviation is Let A and B denote the events described below. Event A: The mean height in a random sample of 16 people is within of the population mean. Event B: The mean height in a random sample of 50 people is within of the population mean. True or false, the probability of event A is greater than the probability of event B? (1 in)

false

Areas under the standard normal curve can be negative.

false

The mean height for a population is 65 inches with a standard deviation of 3 inches. Let A and B denote the events below: A = The mean height in a random sample of 25 is within 1 standard deviation of the population mean. B = The mean height in a random sample of 36 is within 1 standard deviation of the population mean. True or false: The probability of event A is greater than the probability of event B.

false

Suppose you are given two events A and B. It is known that P(A and B) = P(A)xP(B); that is P(A and B) = P(A) times P(B). Based on this information, the two events A and B are definitely

independent

Fill in the blanks by standardizing the normally distributed variable. Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 36 minutes and a standard deviation of 5 minutes. The percentage of time that his commute time is less than 25 minutes is equal to the area under the standard normal curve that lies to the ___ of __.

left, -2.2

For samples of the specified size from the population described, find the mean and standard deviation of the sample mean x bar . The mean and the standard deviation of the sampled population are, respectively, 45.4 and 5.6. n = 196

mean x bar: 45.4 SD x bar=0.4

The U.S. Department of Agriculture often reports the average American consumption of cheese is 33.0 lb. A random sample of 20 people found they consumed an average of 35.0 lb of cheese per year with a standard deviation of 2.4 lb. In this problem, the value 33.0 lb is

mu

For samples of the specified size from the population described, find the mean and standard deviation of the sample mean . The National Weather Service keeps records of rainfall in valleys. Records indicate that in a certain valley, the annual rainfall has a mean of and a standard deviation of Suppose the rainfalls are sampled during randomly picked years and is the mean amount of rain in these years. For samples of size 25, determine the mean and standard deviation of x bar

mu subscript x bar = 93 ; SD subscript x bar= 2

For samples of the specified size from the population described, find the mean and standard deviation of the sample mean . One truck from Lakeland Trucking, Inc. can carry a load of 2855 lb. Records show that the weights of boxes that it carries have a mean of and a standard deviation of For samples of size 25, find the mean and standard deviation of . (x-bar, 110 lb; 10 lb; x-bar)

mu x bar: 110 sd x bar: 2

For samples of the specified size from the population described, find the mean and standard deviation of the sample mean . The mean and the standard deviation of the sampled population are, respectively, 45.4 and 5.6. n = 196

mu x bar: 45.4 SD x-bar: 0.4

For samples of the specified size from the population described, find the mean and standard deviation of the sample mean x bar. The National Weather Service keeps records of rainfall in valleys. Records indicate that in a certain valley, the annual rainfall has a mean of 93 inches and a standard deviation of 10 inches. Suppose the rainfalls are sampled during randomly picked years and is the mean amount of rain in these years. For samples of size 25, determine the mean and standard deviation of x bar

mu x-bar: 93 SD x-bar: 2

Suppose there are two events, A and B. It is known that P(A and B) = 0. This means that A and B are definitely

mutually exclusive

Fill in the blanks by standardizing the normally distributed variable. Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. The percentage of time that his commute time exceeds 61 minutes is equal to the area under the standard normal curve that lies to the ___ of ___.

right, 3.2

The U.S. Department of Agriculture often reports the average American consumption of cheese. A random sample of 20 people found they consumed an average of 35.0 lb of cheese per year with a standard deviation of 2.4 lb. In this problem, the value 2.4 lb is

s

Areas under the standard normal curve cannot be negative

true

In general, the sampling error increases as the sample size decreases.

true

Provide an appropriate response. The mean height for a population is 65 inches and the standard deviation is Let A and B denote the events described below. Event A: The height of a randomly selected person is or more from the population mean. Event B: The mean height in a random sample of 16 people is or more from the population mean. True or false, the probability of event A is greater than the probability of event B? (5 inches)

true

The mean height for a population is 65 inches with a standard deviation of 3 inches. Let A and B denote the events below: A = The mean height in a random sample of 36 is within 1 standard deviation of the population mean. B = The mean height in a random sample of 25 is within 1 standard deviation of the population mean. True or false: The probability of event A is greater than the probability of event B.

true