stats ch 2 test review (Just Q&A)

A score's percentile is a measure of

relative location

the density curve below shows the distribution of a variable that takes values from 0 to 1. What percent of the observations lie between 0 and 0.5

25%

Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. The proportion of infants with birthweights between 125 oz. and 140 oz. is about

0.136.

The Normal curve below describes the death rates per 100,000 people in developed countries in the 1990's. The mean and standard deviation of this distribution are approximately

Mean 190; Standard Deviation 65

an ecologist studying starfish populations 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 frequency distribution for the arm length of 102 Pisaster individuals

Median is 15.2; Intequartile range is 4.3

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

The plot shown below is a Normal probability plot for the total annual cost (tuition plus room and board). to attend 126 of the top colleges in the country in 2005. Which statement is true for these data?

The data are clearly skewed to the left.

When a basketball player makes a pass to a teammate who then scores, he earns an "assist." Below is a Normal probability plot for the number of assists earned by all players in the National Basketball Association during the 2010 regular season. Which of the following statements about the shape of this distribution is true?

The distribution is skewed.

Use Scenario 2-1. The median salary for the employees working for the company will

be multiplied by $3,000.

A standard score describes

how far a particular a score is from the mean

The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?

44

IQs among undergraduates at Mountain Tech are approximately Normally distributed. The mean undergraduate IQ is 110. About 95% of undergraduates have IQs between 100 and 120. The standard deviation of these IQs is about

5.

The five-number summary of the distribution of 316 scores on a statistics exam is: 0 26 31 36 50 The scores are approximately Normal. The standard deviation of test scores must be about

7.5

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

E

The distribution of household incomes in a small town is strongly skewed to the right. The mean income is $42k and the standard deviation is $24k. The Ames family's household income is $60k. The z-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 1.1 is

0.8643.

Consider the following cumulative relative frequency graph of the scores of students in an introductory statistics course

20%

A company produces packets of soap powder that are 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 0.7 oz. 95% of packets actually contain more than x oz. of soap powder. What is x?

31.85

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"

Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack's mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Jill's mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Jack gets a score of 14,000, and Jill gets a score of 16,000. Who won the contest, and what were each of their z-scores?

Jack's z = 1.07; Jill's z = 0.90; Jack wins the contest

Use Scenario 2-1. The z-scores of the salaries for the employees will

be unchanged

Use Scenario 2-1. The interquartile range of the salaries for the employees will

be unchanged.

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

You are told that your score on an exam is at the 85 percentile of the distribution of scores. This means that

your score was higher than approximately 85% of the people who took this exam

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, the resulting scores will have a distribution that has

a mean of 0 and a standard deviation of 1.

Use Scenario 2-1. The standard deviation of the salaries for the employees will

be unchanged.

The fifth number summary of the distribution of scores on the final exam in Psych 001 last semester was: 18, 39, 62, 76, 100

between 76 and 100

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 with a mean of 110 oz. and a standard deviation of 15 oz. The proportion of infants with birthweights under 95 oz. is about

0.159.

Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing 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 Normal distribution tables, the area under the standard Normal curve corresponding to -0.5 < Z < 1.2 is

0.5764.

Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to Z -1.22 is

0.8888.

Suppose that scores on a certain IQ test are Normally distributed with mean 110 and standard deviation 15. Then about 40% of the scores are between

102 and 118.

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 seconds.

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

A soft-drink machine can be regulated so that it discharges an average of ? oz. per cup. If the ounces of fill are Normally distributed with a 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

Here is a list of exam scores for Mr. Williams's calculus class: 60, 61, 61, 65, 72, 75, 75, 78, 81, 81, 85, 89, 91, 98 What is the percentile of the person whose score was 85?

71%

You are chatting with the principal of a local high school. The topic of SAT scores comes up, and the principal mentions that SAT scores at the school are Normally distributed. She doesn't remember the mean or the standard deviation, but she does remember that the upper and lower quartiles are 500 and 600. The standard deviation of SAT verbal scores is closest to

75 points

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 mins

The risk of an investment is measured by the variability of the changes in its value over a fixed period, such as a year. More variation from year to year means more risk. The government's Securities and Exchange Commission wants to require mutual funds to tell investors how risky they are. A news article (New York Times, April 2, 1995) says that some people think that "the proposed risk descriptions, especially one that goes by the daunting name standard deviation" are hard to understand. Explain to a friend what the standard deviation means, using the fact that the changes in a mutual fund's value over many years have a roughly Normal distribution.

Start with the average (mean) change in the fund's value over many years; the actual change will be within one standard deviation of that average in about 68% of all years.

For the density curve below, which of the following is true

The median is larger than 0.5

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

Use Scenario 2-1. The mean salary for the employees will

increase by $3,000.

A stemplot of a set of data is roughly symmetric, but the data do not even approximately follow the 68-95-99.7 rule. We conclude that the data are

not normal

If 30 is added to every number on a list, the only one of the following that is not changed is

the standard deviation.