Math 10 Exam 2

(PLS SHOW WORK and ANSWER ALL THE QUESTIONS ---- NO EXCEPTION) (NOTE: your answer should be among the multiple choice questions/ answer if it's it means your is wrong so pls do your correctly and carefully!!!!!) NO MADE UP ANSWERS PLS AND THANK YOU!!!!!)

Question 1

Assume that X is a normally distributed random variable whose mean is = 44.5 and standard deviation is = 12.7. Find P(X > 71.4).

A.) 0.9830

B.) 0.0235

C.) 0.9765

D.) 0.0170

E.) 0.0204

Question 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.) 0.0987

C.) 0.4013

D.) 0.3821

E.) 0.9013

Question 3

The following are drying times (in minutes) for an adhesive product. 85.7 101.4 91.6 83.5 96.2 88.0 103.6 97.9

A.) 7.42

B.) 7.54

C.) 7.66

D.) 7.83

E.) 7.71

Question 4

A random sample of 34 observations is taken from a population with a mean of 713 and a standard deviation of 85. If the mean of the sample is 676, find the standard score (z score) for this observed sample mean.

A.) -2.29

B.) -2.60

C.) -2.35

D.) -2.48

E.) -2.54

Question 5

The finishing times for a running competition have a normal distribution with a mean of 490 seconds and a standard deviation of 50 seconds. What time is needed to finish in the fastest 10% of runners in this competition?

A.) 443 sec

B.) 432 sec

C.) 426 sec

D.) 451 sec

E.) 554 sec

Question 6

A store manager kept track of the number of newspapers sold each month. The results are shown below. Find the median of the data. 482 339 404 515 387 351 424 467 376 411 392 365

A.) 412

B.) 402

C.) 398

D.) 394

E.) 406

Question 7

A graduate program takes an average of 4.6 years to complete. Assuming completion times are normally distributed with a standard deviation of 1.3 years, find the limits for the middle 60% of completion times for the program.

A.) Between 3.9 years and 5.3 years

B.) Between 4.3 years and 4.9 years

C.) Between 3.5 years and 5.7 years

D.) Between 3.7 years and 5.5 years

E.) Between 3.3 years and 5.9 years

Question 8

Follow-up studies are conducted on patients in a research cohort whose blood pressures are in the top 25% of the cohort. If the patients in the cohort have blood pressures that are normally distributed with mean 131 and standard deviation 14, what is the cutoff for a patient's blood pressure to qualify for a follow-up study?

A.) 145

B.) 139

C.) 141

D.) 122

E.) 143

Question 9

On the latest sociology exam, the class average was 77 with a standard deviation of 4.5. If the z-score for a student's exam was -2.9, what was the student's exam score? Assume exam scores are approximately normally distributed.

A.) 72

B.) 68

C.) 64

D.) 90

E.) 86

Question 10

Assume that the weights of quarters are normally distributed with a mean of 5.55 g and a standard deviation 0.049 g. A vending machine will only accept coins weighing between 5.43 g and 5.67 g. What percentage of legal quarters will be rejected?

A.) 0.0157%

B.) 0.0142%

C.) 1.65%

D.) 1.42%

E.) 1.57%

Question 11

In one region, the average furnace repair bill is $274 with a standard deviation of $32. What is the probability that the average for a sample of 50 such furnace repair bills is between $270 and $280?

A.) 0.1270

B.) 0.2812

C.) 0.0236

D.) 0.7188

E.) 0.8730

Question 12

Assume that X is a normally distributed random variable whose mean is = 48.7 and standard deviation is = 16.3. Find P(55.6 < X < 82.8).

A.) 0.3391

B.) 0.3435

C.) 0.3007

D.) 0.3189

E.) 0.3226

Question 13

Find the probability of getting at least 50 heads in 100 tosses of a coin. Use the normal approximation to the binomial distribution.

A.) 0.5793

B.) 0.5277

C.) 0.5398

D.) 0.5000

E.) 0.4602

Question 14

The annual precipitation for one location is normally distributed with a mean of 52.7 inches and a standard deviation of 3.6 inches. Use the empirical rule to estimate the probability that the annual percipitation in this location will be between 45.5 inches and 56.3 inches.

A.) 90%

B.) 99.7%

C.) 81.5%

D.) 95%

E.) 77.5%

Question 15

On average students take 5.1 years to complete a bachelor's degree. Assuming completion times are normally distributed with a standard deviation of 0.8 year, what is the probability that a student takes longer than 7 years to graduate?

A.) 0.0131

B.) 0.9894

C.) 0.0106

D.) 0.9913

E.) 0.0087

Question 16

The birthweight of newborn babies is normally distributed with a mean of 7.5 pounds and a standard deviation of 1.2 pounds. If a baby has a birthweight of 8 pounds, how many standard deviations from the mean is that.

A.) 0.15 standard deviations above the mean

B.) 6.7 standard deviations above the mean

C.) 6.7 standard deviations below the mean

D.) 0.42 standard deviations below the mean

E.) 0.42 standard deviations above the mean

Question 17

The average selling price for a certain model commerical grade copier is $20,200 with a standard deviation of $375. What is the probability that the mean selling price for a sample of 30 of these copiers exceeds $20,000?

A.) 18%

B.) 99.82%

C.) 9.876%

D.) 98.76%

E.) 0.18%

Question 18

If 5% of customers return the items purchased at a store, find the probability that in a random sample of 1000 customers, fewer than 40 returned the items purchased. Use the normal approximation to the binomial distribution.

A.) 0.0643

B.) 0.0951

C.) 0.0548

D.) 0.0838

E.) 0.0735

Question 19

The time for a certain medication to take effect is normally distributed with a mean of 15 minutes and a standard deviation of 1.9 minutes. For a randomly selected patient, find the probability that the medication will take effect between 10 and 15 minutes.

A.) 0.93

B.) 0.07

C.) 0.5043

D.) 0.4957

E.) 0.0043

Question 20

The average replacement time for washing machines is 9.3 years with a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9 years.

A.) 0.9887

B.) 0.5113

C.) 0.4887

D.) 0.0113

E.) 0.1130