MATH 533 Final Exam Questions – Answered

(TCO A) A random sample of 20 cars driving down I-294 is selected and their speed is monitored.  The results are as follows (in mph).

68           65           50           79           77           60           55

61           78           75          

75           67           72           58           70           62           67

72           70           74

  1. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on speed per car.
  2. In the context of this situation, interpret the Median, Q1, and Q3. (Points: 33)

Answers:

Mean    StDev   Minimum     Q1   Median     Q3    Maximum            Mode

67.75   8.04    50.00     61.25   69.00   74.75    79.00        67, 70, 72, 75

  1. The Median value is 69 implying that 50% of the values are less than or equal to 69 and other 50% is more than 69. The Q1 value is 61.25 implying that 25% of the values are less than or equal to 61.25 and other 75% is more than 61.25. And the Q3 value is 74.75 implying that 75% of the values are less than or equal to 74.75 and other 25% is more than 74.75.

(TCO B) Consider the following data on newly hired employees in relation to which part of the country they were born and their highest degree attained.

HS BS MS PHD Total
East 3 5 2 1 11
Midwest 7 9 2 0 18
South 5 8 6 2 21
West 1 7 8 6 22
Total 16 29 18 9 72

Of you choose one person at random, then find the probability that the person

  1. Has a PHD
  2. is from the East and has a BS as the highest degree arraigned
  3. has only a HS degree, given that person is from the West. (Points: 18)

Answers:

  1. P(Has a PHD) = 9/ 72 = 0.125
  2. P(East and BS) = 5/72 = 0.0694
  3. P(HS|West) = P(HS and West)/P(West) = (1/72)/(22/72) = 1/22 = 0.0455

(TCO B) Midwest Airlines has had an 80% on time departure rate.  A random sample of 20 flights is selected.  Find the probability that

  1. exactly 15 flights depart on time in the sample
  2. at least 17 flights depart on time in the sample
  3. less than 11 flights depart on time in the sample. (Points: 18)

Answers:

Here,

X = Number of flights depart on time out of 20 ~Binomial(n=20,p=0.8)

  1. The obtained Minitab output is as follows,

Probability Density Function

Binomial with n = 20 and p = 0.8

x  P( X = x )

15    0.174560

Thus required probability is 0.174560.

  1. The obtained Minitab output is as follows,

Cumulative Distribution Function

Binomial with n = 20 and p = 0.8

x  P( X ≤ x )

16    0.588551

As P(X≥17) = 1-P(X≤16) thus required probability is (1-0.588551)= 0.411449.

  1. The obtained Minitab output is as follows,

Cumulative Distribution Function

Binomial with n = 20 and p = 0.8

x  P( X ≤ x )

10   0.0025948

As P(X < 11 ) = P(X≤10) thus required probability is 0.0025948.

(TCO B) The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls.  The distribution of mean response times to fire calls follows a normal distribution with a mean of 12.8 minutes and a standard deviation of 3.7 minutes.

  1. Find the probability that a randomly selected response time is less than 15 minutes.
  2. Find the probability that a randomly selected response time is less than 13 minutes.
  3. The fastest 20% of fire departments will be singled out for a special safety award. How fast must a fire department be I order to qualify for the special safety award?  (Points: 18)

Answers:

  1. The obtained Minitab output is given below,

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