# 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**

**Compute the mean, median, mode, and standard deviation, Q****1, Q****3, Min, and Max for the above sample data on speed per car.****In the context of this situation, interpret the Median, Q****1, and Q****3. (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

- 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**

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

**Answers:**

- P(Has a PHD) = 9/ 72 = 0.125
- P(East and BS) = 5/72 = 0.0694
- 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**

**exactly 15 flights depart on time in the sample****at least 17 flights depart on time in the sample****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)

- 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.

- 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.

- 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.**

**Find the probability that a randomly selected response time is less than 15 minutes.****Find the probability that a randomly selected response time is less than 13 minutes.****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:**

- The obtained Minitab output is given below,