BIT 2405 Test 1

It is given that event E has a probability of 0.56. What is the probability of the complement of event E?

.44

HOME RUNS The probability distribution for the number of home runs VT Softball hits per game is given below. Number of Home Runs Probability 0 0.10 1 0.15 2 0.30 3 0.40 4 0.05 What is the probability that in a given game VT will hit 0 home runs?

0.1

Hardluck Harry has a batting average of 0.200 (i.e., a twenty percent chance of a hit each time he's at bat). Scouts for a rival baseball club secretly observe Harry's performance in 10 randomly times at bat. What is the probability that Harry will get at least three hits?

0.3222

Consider a set of data in which the sample mean is 94.2 and the sample standard deviation is 7.8. Calculate the z-score given that x = 97.6. Round your answer to two decimal places.

0.44

Given 2 events A and B, and that P(A)=0.54, P(B)=0.65, P(A U B)=0.70. Find the probability P(A∩B).

0.49

MongoMillions is a lottery game played in the United States. The way the game is played, numbers picked for the prizes consist of 5 numbers picked at random from a pool of 80 numbers (the White Numbers). Then a single number (the Mongo Number) is picked from a second pool of 25 numbers. If the results of these random number selections match one of the winning combinations in any order on your lottery ticket, then you win something. The payout structure is as follows: Match Payout All Six Jackpot 5 White numbers + No Mongo Number $1,000,000 4 out of 5 White + Mongo Number $50,000 4 out of 5 White + No Mongo Number $5,000 3 out of 5 White Numbers + Mongo Number $500 3 out of 5 White Numbers + No Mongo Number $50 2 out of 5 White Numbers + Mongo Number $5 1 out of 5 White Numbers + Mongo Number $3 Mongo Number $1 What are the odds of winning $50,000 for the drawing?

1 in 1602668

3 POINTERS The probability distribution for the number of 3-point goals Tanner makes per game is given below. Number of 3-Point Goals Probability 0 0.10 1 0.25 2 0.40 3 0.20 4 0.05 The expected number of 3-point goals Tanner makes per game is

1.85

In a certain shipment of 1010 phones, 55 are defective. 99 of the phones are selected at random without replacement. What is the probability that 55 of the 99 phones are defective? Express your answer as a fraction or a decimal number rounded to four decimal places.

1/2

A coordinator will select 44 songs from a list of 55 songs to compose an event's musical entertainment lineup. How many different lineups are possible?

120

77 cards are drawn from a standard deck of 5252 playing cards. How many different 77-card hands are possible if the drawing is done without replacement?

133784560

Suppose annual salaries for sales associates from a particular store have a mean of $29,175 and a standard deviation of $1,753. If we don't know anything about the distribution of annual salaries, what is the maximum percentage of salaries above $31,983? Round your answer to two decimal places and report your response as a percentage (eg: 95.25)

38.97%

A sample of 25 observations has a standard deviation of 4. The sum of the squared deviations from the sample is:

384

A brand of automobile comes in five different styles, with four types of engines, with two types of transmissions, and in eight colors. How many autos would a dealer have to stock if he included one for each style-engine-transmission combination?

40

FACTORIES R US The number of sick days for 195 workers taken each month at Factories R Us is summarized below. Number of Sick Days Frequency 0 — 5 89 6 — 10 66 11 — 15 32 16 — 20 8 The percentage of workers taking 0 — 5 sick days was

45.641%

The newly elected president needs to decide the remaining 4 spots available in the cabinet he/she is appointing. If there are 10 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

5040

Given the following data, find the percentile of a weight of 8.1 pounds. Weights of Newborn Babies (in Pounds) 5.6 9.2 9.4 8.6 5.5 5.9 6.6 8.0 7.0 7.0 7.37.3 6.7 5.6 8.2 5.7 6.0 8.6 6.1 9.5 8.0

70

Suppose that prices of recently sold homes in one neighborhood have a mean of $225,000 with a standard deviation of $7100. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $203,700 and $246,300? Round your answer to one decimal place.

88.9%

Suppose it is known that verbal SAT scores have a bell-shaped distribution with a mean of 500 and standard deviation of 100. Approximately what percentage of verbal SAT scores are between 200 and 800?

99.7%

TESTS 2 Suppose Beth scored 87 on her BIT test and 96 on her ACIS test. The statistics for the two tests are in the following table. Course Mean Standard Deviation BIT 75 13 ACIS 83 14 Define "performance" as Beth's score relative to the population. Assume Beth's z-scores for her tests are: BIT = 0.92 and ACIS = 0.93. The best description of Beth's performance on the two tests is:

Beth's performance on her ACIS test is better than her performance on her BIT test

A company has given you the task to research the salary of first year teachers at the local elementary school. Would you be more interested in looking at the mean, median, or mode?

Mean

Determine if there is an outlier in the given data: 12, 11, 9, 25, 13, 24, 46, 27, 6, 55, 44, 49, 21, 5

No outliers

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the 10-day period

must be at least zero

Suppose a basketball player has made 207 out of 345 free throws. If the player makes the next 3 free throws, I will pay you $28. Otherwise you pay me $9. Find the expected value of the proposition. (If your expected value is that I pay you, your answer is positive. If your expected value is that you pay me, then your answer is negative.)

−1.01

BUY MORE The probability distribution for the daily sales at Buy More stores is given below. Daily Sales Probability $40,000 0.1 $50,000 0.3 $60,000 0.4 $70,000 0.2 The probability of having daily sales of at least $50,000 is

0.9

A quality control inspector has drawn a sample of 1818 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that exactly 5 bulbs from the sample are defective? Round your answer to four decimal places.

0.1507

A pizza delivery company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 21022102 customers. The data is summarized in the table below. Gender and Residence of Customers Males Females Apartment 207207 221221 Dorm 292292 6060 With Parent(s) 286286 123123 Sorority/Fraternity House 192192 288288 Other 186186 247247 Copy Data What is the probability that a customer is female and lives in 'Other' or is male and lives in a fraternity house? Express your answer as a fraction or a decimal number rounded to four decimal places.

0.2088

A box contains 14 large marbles and 11 small marbles. Each marble is either green or white. 6 of the large marbles are green, and 4 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or white? Express your answer as a fraction or a decimal number rounded to four decimal places.

0.7600

A real estate agent has 12 properties that she shows. She feels that there is a 40% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling more than 3 properties in one week. Round your answer to four decimal places.

0.7747

A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 9 insects is exposed to the insecticide in a particular experiment. What is the probability that less than 5 insects will survive?

0.901

Ninety percent of automobiles in Montgomery County have both headlights working. What is the probability that in a sample of fifteen automobiles, at least ten will have both headlights working?

0.9978