MidTerm Stat 160	Spring Term 2004	Feb. 24 th	NAME:
	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).

$\{4, 5, 6\}$

(b).

$\{1, 2, 3\}$

(c).

$\{1, 2, 3, 4, 5, 6\}$

(d).

$\{1, 2, 3, 4\}$

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).

$\widehat{p}$ = 0.25

(b).

$\widehat{p}$ = 0.7

(c).

$\widehat{p}$ = 0.3

(d).

$\widehat{p}$ = 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:

$$\mbox{ $\widehat{Y} = -419.85 +6.72X $\space and $R^{2}=89.13$ }\;.$$

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).

$P(A \mbox{ and } B) = P(B)$

(b).

The second card is also an ace.

(c).

P(B|A) = P(B)

(d).

The cards are fair.