stats chapter 2

Items produced by a manufacturing process are supposed to weigh 90 grams. The manu facturing process is such, however, that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights can be approximated by a Normal distribution with mean 90 grams and a standard deviation of 1 gram. About what percentage of the items will either weigh less than 87 grams or more than 93 grams?

0.3%

A company produces ceramic floor tiles that are supposed to have a surface area of 16.0 square inches. Due to variability in the manufacturing process, the actual surface area has a Normal distribution with a mean of 16.1 square inches and a standard deviation of 0.2 square inches. The proportion of tiles produced by the process with surface area less than 16.0 square inches is

0.3085

using the standard distribution tables, the area under the standard normal curve corresponding to -0.5 <Z<1.2

0.5764

The distribution of household incomes in a small town is strongly skewed to the right. The mean income is $42,000 and the standard deviation is $24,000. The Ames family's household income is $60,000. The 2-score for the Ames family's income is

0.75

Using the standard Normal distribution tables. the area under the standard Normal curve corresponding to Z> -1.22

0.8888

Let X denote the time taken for a computer link to be made between the terminal in an executive's office and the computer at a remote factory site. It is known that X has a Normal distribution with a mean of 15 seconds and a standard deviation of 3 seconds. On 90% of the occasions the computer link is made in less than

18.84

Consider the following cumulative relative frequency graph of the of students in an introductory statistics course: grade of C or C+ is assigned to a student who scores between 55 and 70. The percentage of students who obtained a grade of C or C+ is

20%

Entomologist Heinz Kaefer has a colony of bongo spiders in his lab. There are 1000 adult spiders in the colony, and their weights are Normally distributed with mean 11 grams and standard deviation 2 grams. About how many spiders are there in the colony which weigh more than 12 grams?

310

If the heights of 99.7% of American men are between 5'0" and 7'0", what is your estimate of the standard deviation of the height of American men?

4"

A soft-drink machine can be regulated so that it discharges an average of u oz. per cup. If the ounces of fill are Normally distributed witha standard deviation of 0.4 oz., what value should be set at so that 98% of 6-oz. cups will not overflow?

5.18

The 35th percentile of a population is the number x such that

65% of the population scores are above x

The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?

78.4 minutes

The mean number of days that the midge Chaoborus spends in its larval stage is 14.1 days, with a standard deviation of 2.2 days. This distribution is skewed toward higher values. What is the z-score for an individual midge that spends 12.7 days in its larval stage?

-0.64

A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a Normal distribution with a mean of 33 oz. and a standard deviation of 0.8 oz. What proportion of packets are underweight (i.e., weigh less than 32 oz.)?

0.106

Birthweights at a local hospital have a Normal distribution witha mean of 110 oz. and a standard deviation of 15 oz. Which of the following is the proportion of infants with birthweights between 125 oz. and 140 oz.?

0.135

Which of the following dot plots would best be approximated by a Normal distribution?

E

A standard score describes

How far a particular score is from the mean

A data set is Normally distributed with a mean of 25 and a standard deviation of 8. If you calculate the standard score of every observation in this data set, what will the mean and standard deviation of the resulting scores be?

Mean=0; standard deviation=1

Ramon is planning on buying a new car. He's looking at the Ford Escape-a sport-utility vehicle-which gets 28 highway miles per gallon, and the Ford Fusion-a mid-sized sedan-which gets 31 highway miles per gallon. The mean fuel efficiency for all sport utility vehicles is 23, with a standard deviation of 7.6. The mean of all mid-sized sedans is 27, with a standard deviation of 5.2. Which vehicle has a better standing, relative to others of the same style?

The Ford Fusion sedan has a better relative standing, because it's z-score is higher

Scenario 2-1 A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for thiss year. For convenience, the data are ordered 28 31 34 35 47 37 41 42 42 42 49 51 52 52 60 61 67 72 75 77 Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). Use Scenario 2-1. The standard deviation of the salaries for the employees will

be unchanged

Scenario 2-1 A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for thiss year. For convenience, the data are ordered 28 31 34 35 47 37 41 42 42 42 49 51 52 52 60 61 67 72 75 77 Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). use scenario 2-1. the z-scores of the salaries for the employees will

be unchanged z

The five-number summary of the distribution of scores on the final exam in Psych 001 last semester was: 18 39 62 76 100. Which of the following best describes the location of the 80th percentile?

between 76 and 100

Scenario 2-1 A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for thiss year. For convenience, the data are ordered 28 31 34 35 47 37 41 42 42 42 49 51 52 52 60 61 67 72 75 77 Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000). Use Scenario 2-1. The median salary for the employees working for the company will

increased by $3,000

An ecologist who was studying starfish popu lations collected starfish of the species Pisaster was interested in the distribution of sizes of starfish on a certain shoreline. One measure of size is "arm length." Below is a cumulative relative frequency distribution for the arm length of 102 Pisaster individuals

median is 15.2; interquartile range is 3.7

score's percentile is a measure of

relative location

You can roughly locate the mean of a density curve by eye because it is

the point at which the curve would balance if made of solid material

You can roughly locate the median of a density curve by eye because it is

the point that divides the area under the curve into two equal parts

if 30 is added to every number on a list, which one does not change

the standard deviation