Math 10 Practice Exam 2

(PLS SHOW WORK and ANSWER ALL THE QUESTIONS ---- NO EXCEPTION)

Question 1: If 2% of people have green eyes, find the probability that in a random survey of 1000 people more than 25 have green eyes. Use the normal approximation to the binomial distribution.

A.) 8.69%

B.) 10.75%

C.) 15.39%

D.) 12.92%

E.) 7.08%

Question 2

On the latest pharmacology exam, the class average was 76 with a standard deviation of 3.5. If the z-score for a student's exam was -2.3, what was the student's exam score? Assume exam scores are approximately normally distributed.

A.) 84

B.) 76

C.) 68

D.) 64

E.) 72

Question 3

Light sensors are manufactured that have error rates which are normally distributed with a mean of 0 lumens and a standard deviation of 0.71 lumens. Only sensors having error rates between -1.5 lumens and 1.6 lumens are accepted. What percentage of manufactured sensors are rejected?

A.) 2.12%

B.) 1.55%

C.) 2.57%

D.) 1.77%

E.) 2.96%

Question 4

The height of males in the U.S. is normally distributed with a mean of 70 inches and a standard deviation of 3 inches. If a truck designer wishes to build cabs that accommodate the middle 90% of men, find the range of heights the cab should accommodate.

A.) Between 65 inches and 75 inches

B.) Between 63 inches and 77 inches

C.) Between 69 inches and 71 inches

D.) Between 67 inches and 73 inches

E.) Between 61 inches and 79 inches

Question 5

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

A.) 62.55%

B.) 2.28%

C.) 37.45%

D.) 47.72%

E.) 97.72%

Question 6

A major league baseball game uses an average of 102 baseballs with a standard deviation of 9 baseballs. Assuming baseball use is a normally distributed random variable, find the probability that a game uses less than 90 baseballs.

A.) 8.16%

B.) 9.18%

C.) 8.45%

D.) 8.23%

E.) 8.69%

Question 7

The diastolic blood pressure for men is normally distributed with a mean of 80 mm Hg and a standard deviation of 20 mm Hg. If a man has a diastolic blood pressure of 77 mm Hg, how many standard deviations from the mean is that?

A.) 0.15 standard deviations above the mean

B.) 0.26 standard deviations below the mean

C.) 0.15 standard deviations below the mean

D.) 3.85 standard deviations below the mean

E.) 3.85 standard deviations above the mean

Question 8

The repair costs at a vacuum repair shop are approximately normally distributed with a mean of $72 and a standard deviation of $14. Use the empirical rule to estimate the percentage of repairs costing between $58 and $100.

A.) 81.5%

B.) 95%

C.) 77.5%

D.) 90%

E.) 99.7%

Question 9

Assume that X is a normally distributed random variable whose mean is = 64.5 and standard deviation is = 17.2. Find P(28.4 < X < 91.7).

A.) 0.9081

B.) 0.9250

C.) 0.9162

D.) 0.9429

E.) 0.9575

Question 10

To qualify for a position on a wilderness emergency response team, applicants must be within the fastest 10% of hikers. Times for completing a trial hike are normally distributed with mean 97 minutes and standard deviation 14 minutes. What is the cutoff time that qualifies an applicant for a position on the team?

A.) 115 min

B.) 79 min

C.) 73 min

D.) 130 min

E.) 64 min

Question 11

The ages of the employees of an electronics company that retired last year are shown below. Find the median of the data.

62 61 57 51 63 50 59 53 55 63 62 55 62 57

A.) 58.5

B.) 58

C.) 57

D.) 57.5

E.) 59

Question 12

A hotel has a mean number of daily customers of 147 with a standard deviation of 22. What is the probability that the average number of customers per day for the next 60 days will be less than 140?

A.) 49.31%

B.) 50.69%

C.) 6.90%

D.) 0.69%

E.) 99.31%

Question 13

A random sample of 37 observations is taken from a population with a mean of 625 and a standard deviation of 96. If the mean of the sample is 591, find the standard score (z score) for this observed sample mean.

A.) -2.23

B.) -2.57

C.) -2.15

D.) -2.49

E.) -2.36

Question 14

Assume IQ scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that an adult selected at random has an IQ between 100 and 125.

A.) 75.25%

B.) 45.25%

C.) 54.75%

D.) 66.75%

E.) 95.25%

Question 15

Find the probability of getting at most 100 face cards in 500 draws with replacement from a deck of 52 cards. Use the normal approximation to the binomial distribution.

A.) 0.0455

B.) 0.0367

C.) 0.0571

D.) 0.0516

E.) 0.0409

Question 16

Assume that X is a normally distributed random variable whose mean is = 94.7 and standard deviation is = 30.5. Find P(X < 153.6).

A.) 0.9732

B.) 0.0268

C.) 0.9536

D.) 0.9917

E.) 0.0464

Question 17

Scholarships are awarded to the top 5% of entries in an essay contest. If this year's entries are normally distributed with a mean score of 742 and a standard deviation of 38, what is this year's cutoff to receive a scholarship?

A.) 805

B.) 796

C.) 821

D.) 771

E.) 682

Question 181 pts

The commissions for regional bike dealers last month were recorded. The results are shown below. Find the sample standard deviation of the data.

$2894

$1777

$2144

$4536

$4064

$1786

$3291

$4027

$2784

$3652

A.) $972.7

B.) $953.4

C.) $984.6

D.) $969.7

E.) $944.5

Question 19

If the number of grasshoppers in a crop field averages 57 per row with a standard deviation of 12, find the probability that the mean number of grasshoppers per row for a random sample of 40 rows will exceed 60.

A.) 0.5987

B.) 0.9429

C.) 0.0401

D.) 0.0571

E.) 0.4013

Question 20

The average age of vehicles registered in California is 97 months with a standard deviation of 16 months. Find the probability that the mean age of a sample of 33 vehicles is between 94 and 96 months?

A.) 0.1842

B.) 0.2193

C.) 0.2047

D.) 0.1965

E.) 0.1706