AMU MATH 120 Intro to statistics final exam American Military...

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MATH 120 Intro to statistics final exam question 1.

Consider the data set.

2, 5, 6, 7, 8

(a) Find the range. (Enter an exact number.)

(b) Use the defining formula to compute the sample standard deviation s. (Enter a number. Round your answer to two decimal places.)

(c) Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)

MATH 120 Intro to statistics final exam question 2.

Compute P

. (Enter an exact number.)

MATH 120 Intro to statistics final exam question 3.

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

μ = 28; σ = 4.2 P(x ≥ 30) =

0.3192

MATH 120 Intro to statistics final exam question 4.

Sociologists say that 95% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lowerrated areas of contention). Suppose that six married women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.)

(a) All of them dislike their motherinlaw.

(b) None of them dislike their motherinlaw.

(c) At least four of them dislike their motherinlaw.

(d) No more than three of them dislike their motherinlaw.

MATH 120 Intro to statistics final exam question 5.

Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.

Similarities and Differences in a Random Sample of 375 Married Couples

Number of Similar Preferences Number of Married Couples All four 34 Three 126 Two 121 One 62 None 32 Suppose that a married couple is selected at random.

(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality

preferences in common. (For each answer, enter a number. Enter your answers to 2 decimal

places.)

0 1 2 3 4

(b) Do the probabilities add up to 1? Why should they?

What is the sample space in this problem?

0, 1, 2, 3 personality preferences in common 1, 2, 3, 4 personality preferences in common 0, 1, 2, 3, 4, 5 personality preferences in common 0, 1, 2, 3, 4 personality preferences in common

MATH 120 Intro to statistics final exam question 6.

You are the foreman of the BarS cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the BarS herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms).

x	1 5 11 16 26 36
y	39 47 73 100 150 200

Complete parts (a) through (e), given

2

Σx = 95, Σy = 609, Σx

2

= 2375, Σy

= 81,559, Σx y = 13,777, and r ≈ 0.997.

(a) Make a scatter diagram of the data. (Select the correct graph.)

(b) Verify the given sums Σx, Σy, Σx 2 , Σy 2 , Σx y, and the value of the sample correlation coefficient r.

(For each answer, enter a number. Round your value for r to three decimal places.)

Σx = Σy = Σx 2 =

Σy = Σx y =

r=

(c) Find x , and y . Then find the equation of the leastsquares line = a + b x. (For each answer, enter a number. Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x y

(d) Graph the least squares line. Be sure to plot the point ( correct graph.)

, y ) as a point on the line. (Select the

(e) Find the value of the coefficient of determination r 2 . What percentage of the variation in y can be explained by the corresponding variation in x and the leastsquares line? What percentage is unexplained? (For each answer, enter a number. Round your answer for r 2 to three decimal places. Round your answers for the percentages to one decimal place.)

2

r

=

explained =

unexplained =

%

(f) The calves you want to buy are 10 weeks old. What does the leastsquares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.)

MATH 120 Intro to statistics final exam question 7.

The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.

(a) Are the outcomes on the two cards independent? Why?

(b) Find P(ace on 1st card and ten on 2nd). (Enter your answer as a fraction.)

(c) Find P(ten on 1st card and ace on 2nd). (Enter your answer as a fraction.)

(d) Find the probability of drawing an ace and a ten in either order. (Enter your answer as a fraction.)

Compute C

. (Enter an exact number.)

MATH 120 Intro to statistics final exam question 9.

Raul received a score of 80 on a history test for which the class mean was 70 with a standard deviation of 4. He received a score of 70 on a biology test for which the class mean was 70 with standard deviation 10. On which test did he do better relative to the rest of the class?

biology test

history test

the same

MATH 120 Intro to statistics final exam question 10.

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

μ = 8; σ = 2 P(7 ≤ x ≤ 11) =

MATH 120 Intro to statistics final exam question 11

Find the mean, median, and mode of the data set.

9 6 8 6 7 mean (Enter a number.)

median (Enter an exact number.) mode (Enter an exact number.)

MATH 120 Intro to statistics final exam question 12.

How do college professors spend their time? The National Education Association Almanac of Higher Education gives the following average distribution of professional time allocation: teaching, 52%; research, 19%; professional growth, 3%; community service, 11%; service to the college, 11%; and consulting outside the college, 4%. Make a pie chart showing the allocation of professional time for college professors. (Select the correct graph.)

MATH 120 Intro to statistics final exam question 13

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 45 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $2.00 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop (in dollars). What is the margin of error (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.27 for the mean price per 100 pounds of watermelon. (Enter a number. Round up to the nearest whole number.)

farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop (in dollars). What is the margin of error (in dollars)? Hint: 1 ton is 2000 pounds. (For each answer, enter a number. Round your answers to two decimal places.)

lower limit $ upper limit $ margin of error $

MATH 120 Intro to statistics final exam question 14.

A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6hour period. The percentage data are the percentages of fishermen who caught x fish in a 6hour period while fishing from shore.

x	0 1 2 3 4 or more
%	43% 35% 15% 6% 1%

(a) Convert the percentages to probabilities and make a histogram of the probability distribution. (Select the correct graph.)

(b) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6hour period. (Enter a number. Round your answer to two decimal places.)

(c) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6hour period. (Enter a number. Round your answer to two decimal places.)

(d) Compute μ, the expected value of the number of fish caught per fisherman in a 6hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.) μ = fish

(e) Compute σ, the standard deviation of the number of fish caught per fisherman in a 6hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.) σ = fish

MATH 120 Intro to statistics final exam question 15

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Enter a number. Round your answer to four decimal places.)

The area to the left of z = 0.43 is

.

MATH 120 Intro to statistics final exam question 16.

Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio.

(a) Length of time to complete an exam