MidTerm Stat 160 |
Spring Term 2004 | Feb. 24 th |
NAME: |
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FORM B |

- 1.
- A fair 6-sided dice is rolled. Let the event A be defined as observing a number less than 4. The complement of the event A will be
**(a).****(b).****(c).****(d).**

- 2.
- There are 30 students in a statistics class. The instructor randomly selects 5 students from the class to work together on a special class project. If we simulate 100 selections using resampling, which one of the following would be an appropriate model.
**(a).**Number of trials = 100 Minimum Value = 1 Maximum value = 5 Number to sample = 30 Without replacement

**(b).**Number of trials = 30 Minimum Value = 1 Maximum value = 100 Number to sample = 5 Without replacement

**(c).**Number of trials = 100 Minimum Value = 1 Maximum value = 30 Number to sample = 5 Without replacement

**(d).**Number of trials = 100 Minimum Value = 1 Maximum value = 30 Number to sample = 5 With replacement

**For the next three problems:**

Refer to the following situation and RWEB output:Amateur athletes can complete a 5-mile track in an average of 15 minutes with a standard deviation of 3 minutes.

Rweb:> # NORMAL PERCENTAGE POINT Rweb:> qnorm(0.1, 15, 3) [1] 11.15535 Rweb:> # NORMAL PERCENTAGE POINT Rweb:> qnorm(0.9, 15, 3) [1] 18.84465 Rweb:> # CUMULATIVE NORMAL DISTRIBUTION Rweb:> pnorm(10, 15, 3) [1] 0.0477 Rweb:> # CUMULATIVE NORMAL DISTRIBUTION Rweb:> pnorm(5, 15, 3) [1] 0.0004

- 3.
- What percentage of amateur athletes can complete the track in at most 10 minutes?
**(a)**- 95.22%
**(b)**- 18.84%
**(c)**- 11.16%
**(d)**- 4.77%

- 4.
- What is the probability that an amateur athlete will finish the track in at least 5 minutes?
**(a)**- 0.6667
**(b)**- 0.9522
**(c)**- 0.0004
**(d)**- 0.9996

- 5.
- Below what time does the fastest 10% of the athletes finish the whole track?
**(a)**- 13.85 minutes
**(b)**- 18.84 minutes
**(c)**- 1.5 minutes
**(d)**- 11.15 minutes

- 6.
- In a certain fabricating company, an average of 1 out of 20 items coming off an assemble line is defective. The quality-control supervisor wants to know the probability of two items randomly selected from the assembly line being defective (Assume Independence).
**(a).**- 0.0055
**(b).**- 0.0475
**(c).**- 0.9025
**(d).**- 0.0025

- 7.
- A baseketball player's freethrow average is 60%.
Given 15 attempts,
how many freethrows is he expected to make?
**(a)**- 9
**(b)**- 11
**(c)**- 7
**(d)**- 6

**For the next two problems:**

Consider the experiment of rolling three 6-sided dice at the same time. If you observe atleast two even numbers, its considered a success.Trial 1 4 6 6 Trial 2 3 3 2 Trial 3 3 4 6 Trial 4 1 3 1 Trial 5 1 2 5 Trial 6 2 2 3 Trial 7 5 1 3 Trial 8 1 4 6 Trial 9 5 3 1 Trial 10 5 4 6

- 8.
- Based on the results of 10 trials given below, estimate the probability of success.
**(a).**- = 0.25
**(b).**- = 0.7
**(c).**- = 0.3
**(d).**- = 0.5

- 9.
- What is the error of the estimated probability for the above problem?.
**(a).**- 0.189
**(b).**- 0.1
**(c).**- 0.443
**(d).**- 0.316

- 10.
- Suppose we want to model heights of college students. Which of the following
probability models is most appropriate?
**(a)**- Binomial
**(b)**- Normal
**(c)**- Poisson
**(d)**- Uniform

**For the next three problems**

The table gives the peak power load for a power plant and the daily high temperature for a random sample of 10 days.High temperature Peak load 95 214 82 152 90 156 81 129 99 254 100 266 93 210 95 204 93 213 87 150 Let

*Y*denote the peak load and let*X*denote the high temperature. The least squares procedure gave:

- 11.
- Using the regression equation, predict the peak load of a daily high temperature of 96.
**(a)**- 645.12
**(b)**- 225.27
**(c)**- 204.00
**(d)**- 1064.97

- 12.
- Which of the following is the best interpretation of the slope of the regression equation?
**(a)**- When the daily high temperature increase by 1 degree, peak load increases by 6.72.
**(b)**- When the daily high temperature increase by 1 degree, peak load decreases by 419.85.
**(c)**- When the daily high temperature equals to zero, peak load is -419.85.
**(d)**- It has no practical meaning as
*X*=0 is not in the range of the data.

- 13.
- Compute the interquartile range (IQR) of the peak power load.
**(a)**- 137
**(b)**- 62
**(c)**- 207
**(d)**- 25%

- 14.
- In a color preference experiment, eight toys are placed in a container. The toys are identical except for color - 2 are red, and six are green. A child is asked to choose two toys at random (Without replacement). What is the probability that the child chooses the two red toys?.
**(a).**- 0.2500
**(b).**- 0.0357
**(c).**- 0.9640
**(d).**- 0.5350

**For the next two problems**

How much combustion efficiency should a homeowner expect from an oil furnace. A home-heating contractor who sells oil heaters measured the efficiency ratings in percentages for the twenty heaters and are shown in the stem and leaf plot below:5|9 6|7 8 9 7|2 3 4 4 5 5 5 6 8 8 8|1 2 5 8 8 9

- 15.
- What is the median efficiency ratings of the 20 heaters?
**(a)**- 75.0
**(b)**- 72.5
**(c)**- 81.5
**(d)**- 59.0

- 16.
- What seems to be the shape of the data?
**(a)**- unimodal
**(b)**- right-skewed
**(c)**- symmetric
**(d)**- left-skewed

**For the next three problems:**

Refer to the following situation and the RWEB output:Ten persons enter a department store. From past experience, it is known that 80% of the people entering the department store make a purchase.

Rweb:> # CUMULATIVE BINOMIAL DISTRIBUTION Rweb:> pbinom(7, 10, 0.8) [1] 0.3222 Rweb:> # BINOMIAL PROBABILITY Rweb:> dbinom(7, 10, 0.8) [1] 0.2013 Rweb:> # CUMULATIVE BINOMIAL DISTRIBUTION Rweb:> pbinom(10, 7, 0.8) [1] 1 Rweb:> # CUMULATIVE BINOMIAL DISTRIBUTION Rweb:> pbinom(6, 10, 0.8) [1] 0.1208 Rweb:> # BINOMIAL PROBABILITY Rweb:> dbinom(6, 10, 0.8) [1] 0.0880

- 17.
- What is the probability that exactly 7 of the 10 people will make a purchase?
**(a)**- 1.0000
**(b)**- 0.3222
**(c)**- 0.2013
**(d)**- 0.7000

- 18.
- What is the chance that more than 7 will purchase?
**(a)**- 0.9119
**(b)**- 0.7986
**(c)**- 0.8491
**(d)**- 0.6778

- 19.
- What is the chance that at most 6 will purchase?
**(a)**- 0.2013
**(b)**- 0.0880
**(c)**- 0.1208
**(d)**- 0.8791

- 20.
- Which of the following statements is(are) TRUE?
**I.**- A correlation coefficient equal to zero means that there is no linear relationship between the two variables.
**II.**- In a residual plot, a random scatter indicates a good model.

**(a)**- Both I and II
**(b)**- II only
**(c)**- I only
**(d)**- Neither I nor II

- 21.
- which of the following is NOT true about the sample median?
**(a)**- The sample median is obtained by adding up all the data and dividing by the sample size.
**(b)**- The sample median is not affected by outliers.
**(c)**- 50% of the data is less than the sample median.
**(d)**- The sample median is one of the 5 basic statistic.

**For the next two problems:**

Phone calls arrive at a secretary's line 5 times every half hour.Refer to the folllowing RWEB output:

Rweb:> # CUMULATIVE POISSON DISTRIBUTION Rweb:> ppois(5, 3) [1] 0.9160 Rweb:> # POISSON PROBABILIY Rweb:> dpois(3, 5) [1] 0.1403 Rweb:> # CUMULATIVE POISSON DISTRIBUTION Rweb:> ppois(3, 5) [1] 0.2650 Rweb:> # POISSON PROBABILIY Rweb:> dpois(5, 3) [1] 0.1008 Rweb:> ppois(4, 5) [1] 0.4404 Rweb:> # POISSON PROBABILIY Rweb:> dpois(4, 5) [1] 0.1754

- 22.
- What is the probability that there are at least 4 phone calls arriving in the next 30 minutes?
**(a)**- 0.7350
**(b)**- 0.0940
**(c)**- 0.1750
**(d)**- 0.8250

- 23.
- Find the probability that 3 phone calls will be arriving in the next half hour?
**(a)**- 0.1403
**(b)**- 0.9160
**(c)**- 0.1008
**(d)**- 0.2650

- 24.
- For the next two problems consider the following question.
Two cards are drawn from a deck of 52 cards (With replacement). Let event

*A*be the event the first card is an ace. Let event*B*be the event that the second card is an ace. Calculate the probability that the second card is an ace given the first was an ace.**(a).**- 0.0045
**(b).**- 0.0588
**(c).**- 0.1538
**(d).**- 0.0769

- 25.
- The above two events are independent because
**(a).****(b).**- The second card is also an ace.
**(c).**-
*P*(*B*|*A*) =*P*(*B*) **(d).**- The cards are fair.