Ch 6 Stats

A ferry will safely accommodate 73 tons of passenger cars. Assume that the mean weight of a passenger car is 1.7 tons with standard deviation 0.7 tons. If a random sample of 39 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?

0.0630

Find the probability P(-1.04 < z < 1.11) using the standard normal distribution.

0.7173

A sample of size 85 will be drawn from a population with mean 22 and standard deviation 13. Find the probability that x bar will be between 19 and 23.

0.7446

A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5mpg. A pizza delivery company buys 43 of these cars. What is the probability that the average mileage of the fleet is greater than. 33.5 mpg?

0.7454

A certain car model has a mean gas mileage of 28 miles per gallon (mpg) with a standard deviation 5 mpg? A pizza delivery company buys 37 of these cars. What is the probability that the average mileage of the fleet is between 27.2 and 28.8 mpg?

0.6680

A certain car model has a mean gas mileage of 28 miles per gallon (mpg) with a standard deviation 5mpg. A pizza delivery company buys 37 of these cars. What is the probability that the average mileage of the fleet is between 27.2 and 28.8 mpg?

0.6680

A biologist estimates that 40% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 124 or fewer deer have this tick?

0.702

A certain car model has a mean gas mileage of 28 miles per gallon (mpg) with a standard deviation 4 mpg A pizza delivery company buys 44 of these cars. What is the probability that the average mileage of the fleet is between 27.2 and 28.5 mpg?

0.7050

A certain car model has a mean gas mileage of 28 miles per gallon (mpg) with a standard deviation 4mpg. A pizza delivery company buys 44 of these cars. What is the probability that the average mileage of the fleet is between 27.2 and 28.5 mpg?

0.7050

Find the probability P(z > -0.54) using the standard normal distribution.

0.7054

Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 90, p = 0.41: P(32 < X < 43)

0.7113

Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 78, p = 0.59: P(X > 42)

0.7910

A biologist estimates that 70% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 216 or fewer deer have this tick?

0.794

A sample of size 65 will be drawn from a population with mean 22 and standard deviation 15. Find the probability that will be between 20 and 25.

0.8040

A sample of size 60 will be drawn from a population with mean 23 and standard deviation 8. Find the probability that x bar will be between 22 and 25.

0.8078

The average diameter of sand dollars on a certain island is 3.00 centimeters with a standard deviation of 1.00 centimeters. If 9 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 2.70 centimeters. Assume that the variable is normally distributed.

0.816

The average gas mileage of a certain model car is 26.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.15 miles per gallon, find the probability that a car has a gas mileage of between 25.8 and 26.2 miles per gallon.

0.816

Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 80, p = 0.71: P(53 ≤ X ≤ 66)

0.8470

Find the z-score for which the area to the left is 0.81.

0.88

The average height of flowering cherry trees in a certain nursery is 11.5 feet. If the heights are normally distributed with a standard deviation of 1.7 feet, find the probability that a tree is less than 13.5 feet tall.

0.88

The average diameter of sand dollars on a certain island is 3.00 centimeters with a standard deviation of 1.00 centimeters. If 9 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 2.60 centimeters. Assume that the variable is normally distributed.

0.885

The average height of flowering cherry trees in a certain nursery is 11 feet. If the heights are normally distributed with a standard deviation of 1.6 feet, find the probability that a tree is less than 13feet tall.

0.89

A sample of size 35 will be drawn from a population with mean 35 and standard deviation 13. Find the probability that will be less than 38.

0.9147

A gardener buys a package of seeds. Eighty-one percent of seeds of this type germinate. The gardener plants 120 seeds. Approximate the probability that the number of seeds that germinate is between 89.2 and 105.2 exclusive.

0.9199

Find the area under the standard normal curve to the left of z = 1.5.

0.9332

A sample of size 58 will be drawn from a population with mean 33 and standard deviation 5. Find the probability that x bar will be less than 34.

0.9357

A gardener buys a package of seeds. Seventy-six percent of seeds of this type germinate. The gardener plants 80 seeds. Approximate the probability that the number of seeds that germinate is between 51.8 and 67.8 exclusive.

0.9426

A sample of size 52 will be drawn from a population with mean 18 and standard deviation 13. Find the probability that will be less than 21.

0.9515

Find the area under the standard normal distribution curve to the left of z=1.69

0.9545

Find the area under the standard normal curve that lies between z = -1.9 and z= 2.2

0.9574

A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will admit to reading the newspaper while driving.

1.3%

Find the z value that corresponds to the given area. z=0.0721

1.46

If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is

11.0

If a baseball player's batting average is 0.340 (i.e., the probability of getting a hit each time at bat is 0.340), find the probability that the player will have a bad season and get at most 60 hits in 200 times at bat?

13.1%

X is a normally distributed random variable with a mean of 10.0and a standard deviation of 3.50. Find the value x such that is equal to 0.86. (Note: the diagram is not necessarily to scale.)

13.78

X is a normally distributed random variable with a standard deviation of 1.50. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 9.71. (Note: the diagram is not necessarily to scale.)

8.0

X is a normally distributed random variable with a standard deviation of 2.00. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 10.28. (Note: the diagram is not necessarily to scale.)

8.0

X is a normally distributed random variable with a mean of 5.0 and a standard deviation of 3.00. Find the value x such that is equal to 0.86. (Note: the diagram is not necessarily to scale.)

8.24

Of the members of a Boy Scout troop, 15% have received the first aid merit badge. If 40 boy scouts are selected at random, find the probability that four or more will have the first aid merit badge?

86.6%

Find the z-score for which the area to the right is 0.77.

-0.74

Find the z-score for which the area to the right is 0.37.

0.33

Which of the following characteristics does not apply to a theoretical normal distribution?

It is bimodal

If a normal distribution has a mean of 35 and a standard deviation of 10, then

The median is 35 and the mode is 35

Find the z value that corresponds to the given area. x< 0.4129

-.22

Find the z-score for which the area to the right is 0.52.

-0.05

A gardener buys a package of seeds. Eighty-seven percent of seeds of this type germinate. The gardener plants 90 seeds. Approximate the probability that fewer than 71 seeds germinate.

0.0073

A normal population has a mean μ = 40 and standard deviation What is the probability that a randomly chosen value will be greater than 57?

0.0294

Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 90, p = 0.6: P(X ≥ 63)

0.0336

Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 77, p = 0.33: P(X ≤ 18)

0.0475

A sample of size 36 will be drawn from a population with mean 20 and standard deviation 15. Find the probability that x bar will be greater than 24.

0.0548

A certain car model has a mean gas mileage of 33 miles per gallon (mpg) with a standard deviation 4 mpg. A pizza delivery company buys 47 of these cars. What is the probability that the average mileage of the fleet is greater than 33.8 mpg?

0.0853

A sample of size 37 will be drawn from a population with mean 20 and standard deviation 9. Find the probability that x bar will be greater than 22.

0.0885

A normal population has a mean μ = 33 and standard deviation What is the probability that a randomly chosen value will be greater than 44?

0.1112

The average length of crocodiles in a swamp is 12 feet. If the lengths are normally distributed with a standard deviation of 1.9 feet, find the probability that a crocodile is more than 11.5 feet long.

0.60

Find the z-score for which the area to the left is 0.73.

0.61

The length of country and western songs is normally distributed and has a mean of 160 seconds and a standard deviation of 30 seconds. Find the probability that a random selection of 25 songs will have mean length of 153.58 seconds or less. Assume the distribution of the lengths of the songs is normal.

0.14

The length of country and western songs is normally distributed and has a mean of 200 seconds and a standard deviation of 40 seconds. Find the probability that a random selection of 25 songs will have mean length of 191.44 seconds or less. Assume the distribution of the lengths of the songs is normal.

0.14

Use the normal approximation to the binomial to find that probability for the specific value of X.n = 30, p = 0.7, X = 22

0.15

The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 37. A pollster draws a sample of 42 people to interview. What is the probability that the sample mean income is less than 36 (thousands of dollars)?

0.1894

The mean annual income for people in a certain city (in thousands of dollars) is 45, with a standard deviation of 32. A pollster draws a sample of 49 people to interview. What is the probability that the sample mean income is less than 41 (thousands of dollars)?

0.1922

Use the normal approximation to the binomial to find that probability for the specific value of X.n = 30, p = 0.4, X = 5

0.20

A bottler of drinking water fills plastic bottles with a mean volume of 997 milliliters (mL) and standard deviation 6mL.The fill volumes are normally distributed. What proportion of bottles have volumes less than 992mL?

0.2033

A gardener buys a package of seeds. Eighty-four percent of seeds of this type germinate. The gardener plants 90 seeds. Approximate the probability that 79 or more seeds germinate.

0.2033

Find the area under the standard normal curve that lies outside the interval between z= -0.6 and z= 1.8

0.3102

Find the probability P(0.16 < z < 1.23) using the standard normal distribution.

0.3271

Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 82, p = 0.63: P(X > 53)

0.3372

Find the probability P(z < -0.31) using the standard normal distribution.

0.3783

A bottler of drinking water fills plastic bottles with a mean volume of 1010 milliliters (mL) and standard deviation 7 mL. The fill volumes are normally distributed. What proportion of bottles have volumes greater than 1012 mL.

0.3859

Find the z-score for which the area to the left is 0.66.

0.41

Find the area under the standard normal distribution curve between x=0 and z=-2.16

0.4846

Find the area under the standard normal distribution curve between z = 0 and z = 2.16.

0.4846

The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 34. A pollster draws a sample of 58 people to interview. What is the probability that the sample mean income is between 38 and 44 (thousands of dollars)?

0.4971

Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 98, p = 0.56: P(X < 56)

0.5517

Find the z value that corresponds to the given area. z=0.2157

0.57

Find the probability P(z < 0.37) using the standard normal distribution.

0.6443

The average number of mosquitos in a stagnant pond is 80 per square meter with a standard deviation of 12. If 36 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 81.8 mosquitos per square meter. Assume that the variable is normally distributed.

18.4%

X is a normally distributed random variable with a mean of 8.00. If the probability that X is less than 9.10 is 0.67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.)

2.50

The average number of mosquitos in a stagnant pond is 100 per square meter with a standard deviation of 16. If 9 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 103.7 mosquitos per square meter. Assume that the variable is normally distributed.

24.2%

In order to have the standard error of the mean be 12, one would need to take ________________ samples from a normally distributed population with a standard deviation of 60.

25

The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75?

28.8%

The mean number of pets per household is 2.96 with standard deviation 1.4. A sample of 52 households is drawn. Find the 74th percentile of the sample mean.

3.08

X is a normally distributed random variable with a mean of 5.00. If the probability that X is less than 6.54 is 0.67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.)

3.50

A sample of size 50 will be drawn from a population with mean 73 and standard deviation 8. Find the 19th percentile of x bar .

72.0

X is a normally distributed random variable with a standard deviation of 3.50. Find the mean of X when 64.8% of the area lies to the left of 9.33. (Note: the diagram is not necessarily to scale.)

8. 0

X is a normally distributed random variable with a mean of 5.0. Find the standard deviation of the distribution if 59.10% of the data lies to the right of 4.08. (Note: the diagram is not necessarily to scale.)

4.0

X is a normally distributed random variable with a mean of 10.00. If the probability that X is less than 11.76 is 0.67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.)

4.00

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.9 pounds and standard deviation 1.9pounds. A turkey farmer wants to provide a money-back guarantee that her 6-week poults will weigh at least a certain amount. What weight should she guarantee so that she will have to give her customer's money back only 1% of the time?

4.47 ib

X is a normally distributed random variable with a mean of 6 and a standard deviation of 2.5. Find the value of X for which 70.54% of the area under the distribution curve lies to the right of it. (Note: the diagram is not necessarily to scale.)

4.65

Find the probability P(0 < z < 1.67), using the standard normal distribution.

45.25%

The average age of doctors in a certain hospital is 46.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 6.0 years. If 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 46.6 years. Assume that the variable is normally distributed.

61.8%

Which choice is another term that can be used to describe a normal distribution:

Bell Curve

The area under the normal distribution curve that lies within three standard deviations of the mean is approximately 95%.

False

To find the area under the standard normal distribution curve between two z values, one first finds the difference between the two zvalues, then locates the value corresponding to that difference in the Standard Normal Distribution table.

False

For a normal distribution curve with a mean of 9and a standard deviation of 5, which of the following ranges of the variable will define an area under the curve corresponding to a probability of approximately 34%?

From 9 to 14

Identify the type of distribution pattern that occurs when the majority of the data values fall to the left of the mean?

Positively Skewed

Stating that the area under the standard normal distribution curve between and is 0.3413, is the same as stating that the of randomly selecting a standard normally distributed variable z with a value between 0 and 1.00 is 0.3413.

Probability

One normal curve has a mean of 24 and a standard deviation of 3. A second normal curve has a mean of 3 and a standard deviation of 24. The curve that is more dispersed, or spread out, is

The Second normal curve

Which of the following properties distinguishes the standard normal distribution from other normal distributions?

The mean is 0 and the standard deviation is 1.

In applied statistics, it is the area under the normal distribution curve which is most important, not the value of single points on the curve.

True

The area under a normal distribution curve is always positive even if the z value is negative.

True

The normal distribution curve can be used as a probability distribution curve for normally distributed variables.

True

The probability P(0 < z < 0.97) is 0.3340.

True

When the majority of the data values fall to the right of the mean, the distribution is said to be left-skewed.

True

For a normal distribution curve with a mean of 15 and a standard deviation of 5, which range of the variable defines an area under the curve corresponding to a probability of approximately 68%?

from 10 to 20

The number of standard deviations a particular X value is from the mean is commonly referred to as .

z