Test 2a/Key
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.

1) Rolling a single die 59 times, keeping track of the numbers that are rolled.

A) Not binomial there are more than two outcomes for each trial.

B) Not binomial the trials are not independent.

C) Not binomial there are too many trials.

D) Procedure results in a binomial distribution.

 

Find the indicated probability.

2) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

A) 0.5987

B) 0.3821

C) 0.4013

D) 0.0987

 

Find the mean, m, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.

3) n = 23; p = 3/5

A) m = 13.8

B) m = 13.3

C) m = 14.1

D) m = 14.5

 

Find the standard deviation, s, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth.

4) n = 35; p = 3/5

A) s = 2.90

B) s = 7.02

C) s = 6.17

D) s = 0.49

If z is a standard normal variable, find the probability.

5) P(z > 0.59)

A) 0.2776

B) 0.2190

C) 0.2224

D) 0.7224

 

6) The probability that an observation z falls between 0 and 3.01

A) 0.1217

B) 0.9987

C) 0.4987

D) 0.5013

 

7) P(-0.73 < z < 2.27)

A) 0.7557

B) 0.2211

C) 1.54

D) 0.4884

 

Find the indicated probability.

8) A company finds that an average of 20% of all new employees resign during the first year. Find the probability that among the next 30 employees hired, exactly five resign during the first year.

A) 0.198

B) 0.172

C) 0.067

D) 0.421

 

Solve the problem.

9) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 107 inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 109.8 inches?

A) 0.4192

B) 0.0808

C) 0.5808

D) 0.9192

 

 

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0degreeC at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0degreeC (denoted by negative numbers) and some give readin gs above 0degreeC (denoted by positive numbers). Assume that the mean reading is 0degreeC and the standard deviation of the readings is 1.00degreeC. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information.

10) If 7% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.

A) 1.48

B) 1.45

C) 1.39

D) 1.26

 

Determine if the outcome is unusual.

11) According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 500 pm on Sunday nights. At 500 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be unusual to find that 873 of the 2500 televisions are tuned to "Eyewitness News"?

 

Solve the problem.

12) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find the 40% percentile.

 

Find the indicated probability.

13)

A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 35 that have no defects. What is the probability that at least one of the calculators is defective?

 

Describe the complement of the given event.

14) When 6 diners have lunch, none of them orders liver and onions.

A) When 5 diners have lunch, at least one of them orders liver and onions.

B) When 6 diners have lunch, at least 5 of them order liver and onions.

C) When 6 diners have lunch, at least one of them orders liver and onions.

D) When 6 diners have lunch, all of them order liver and onions.

 

Identify the given random variable as being discrete or continuous.

15) The number of freshmen in the required course, English 101

A) Continuous

B) Discrete

 

Solve the problem.

16) The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one

$3600 (1 chance in 8200); $1200 (1 chance in 6800); $600 (1 chance in 4200); $400 (1 chance in 2400).

Find the expected value of the amount won for one entry if the cost to enter is 57 cents.

A) $ 0.19

B) $ 0.93

C) $ 399.43

D) $ 0.36

Key

1) Answer A

2) Answer C

3) Answer A

4) Answer A

5) Answer A

6) Answer C

7) Answer A

8) Answer B

9) Answer D

10) Answer A

11)

Answer

 

12)

Answer

13)

Answer

 

14) Answer C

15) Answer B

16) Answer D

 

 

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