MidTerm Stat 160 Fall Term 2003 Oct. 21 st NAME: FORM A

1.
A box of nine golf gloves contains two left-handed gloves and seven right-handed gloves. If two gloves are randomly selected from the box without replacement, what is the probability that both gloves selected will be right-handed?

(a)
7/12
(b)
2/7
(c)
5/12
(d)
1/28

2.
Lego pieces are produced with a defective rate of 15% Consider the number of defective pieces in a random sample of 500 lego pieces. Determine the expected value and standard deviation of the number of defective pieces in the sample.
(a).
500, 7.98
(b).
75, 63.75
(c).
75, 7.98
(d).
500, 63.75

3.
In a biological cell the average member of genes that will change into mutant genes, when treated radioactively, is 2.4. Assuming a Poisson probability distribution, find the probability that there are at most 3 mutant genes in a biological cell after the radioactive treatment. Use the following information from RWEB to help answer the question.

```Rweb:> # CUMULATIVE POISSON DISTRIBUTION
Rweb:> ppois(3, 2.4)
[1] 0.7787229

Rweb:> # CUMULATIVE POISSON DISTRIBUTION
Rweb:> ppois(2, 2.4)
[1] 0.5697087

Rweb:> # POISSON PROBABILIY
Rweb:> dpois(2, 2.4)
[1] 0.2612677

Rweb:> # POISSON PROBABILIY
Rweb:> dpois(3, 2.4)
[1] 0.2090142
```

(a).
1.0000
(b).
0.2090
(c).
0.7787
(d).
0.8714

4.
Which of the following probabilities are feasible for an experiment having a sample space ?

(a)
P(s1) =0.25, P(s2) =0.5, P(s3)=0.25
(b)
P(s1) =0.7, P(s2) =0.5, P(s3)=-0.2
(c)
P(s1) =0.5, P(s2) =0.2, P(s3)=1.0
(d)
P(s1) =0.4, P(s2) =0.4, P(s3)=0.4

5.
Let's play pairs! A team consists of two players. Both players will choose a card from a deck of 52 cards and show it. If their cards have the same denomination (kind) (e.g. 2 of spade and 2 of hearts) they win the prize. You decide to perform 500 resampling trials. Which of the following resampling models would be the correct model to simulate the probability of winning?

(a)
```Number of trials = 100
Minimum Value = 0
Maximum value = 52
Number to sample = 2
Without replacement
```

(b)
```Number of trials = 500
Minimum Value = 1
Maximum value = 52
Number to sample = 2
Without replacement
```

(c)
```Number of trials = 500
Minimum Value = 1
Maximum value = 52
Number to sample = 2
With replacement
```

(d)
```Number of trials = 500
Minimum Value = 1
Maximum value = 2
Number to sample = 52
Without replacement
```

For the next two problems: The following output refers to an analysis on the amount of calories burned by 14 randomly selected athletes after performing a new kind of exercise.

```Rweb:> summary(variables)
cal
Min.   :23.00
1st Qu.:31.75
Median :37.00
Mean   :38.57
3rd Qu.:43.50
Max.   :67.00
```

6.
The range and interquartile range respectively are:?
(a)
11.75, 44
(b)
24, 8.75
(c)
lacks sufficient information
(d)
44, 11.75

7.
Which of the following observations is a potential outlier:
(a)
37
(b)
67
(c)
23
(d)
47

For the next three questions: The following data refers to the annual expenditures (exp) and annual incomes (inc) of 9 households. These were measured in thousand of dollars.

 exp inc 23 46 35 78 48 65 34 94 61 127 36 98 66 104 52 89 76 154

We want to predict the annual expenditures of households by looking at the annual incomes. The estimated regression line computed was .

8.
The slope of the line means:
(a)
For every thousand increase in the annual income, the estimate in the expenditure increases by \$0.44.
(b)
For every thousand increase in the annual income, the estimate in the expenditure increases by \$440.
(c)
For every thousand increase in the expenditure, the estimate in the annual income increases by \$440.
(d)
For every thousand increase in the annual income, the estimate in the expenditure increases by \$595.

9.
Using the estimated regression line, predict the annual expenditure of a household earning \$87000 annually:
(a)
\$44,230
(b)
\$87,000.00
(c)
\$38,285.95
(d)
\$18,420.45

10.
Compute the residual of the observation with and
(a)
6.89
(b)
-6.89
(c)
60.17
(d)
0

For the next two problems:

Of the volunteers coming into a blood center, 30% have O+, 10% have O-, 20% have A+, 20% have A- and 20% have other blood type. Let [00-29] = Type O+, [30-39] = Type O-, [40-59] = Type A+, [60-79] = Type A- and [80-99] = Others.

The resampling module was used from Class Code, followed by the output.

```    Number of trials = 12
Minimum Value = 0
Maximum value = 99
Number to sample = 5
Without replacement

Trial 1
42      57      59      82      85

Trial 2
23      43      49      62      85

Trial 3
1       5       29      83      92

Trial 4
43      54      60      71      88

Trial 5
8       35      40      48      52

Trial 6
41      43      47      60      95

Trial 7
37      51      66      67      76

Trial 8
25      28      55      75      78

Trial 9
20      47      54      75      99

Trial 10
11      13      27      33      55

Trial 11
29      46      51      59      90

Trial 12
18      37      40      49      52
```

11.
Estimate the probability that out of 5 donors, 3 of them have A+ type blood.
(a)
0.50
(b)
0.42
(c)
0.25
(d)
0.20

12.
What is the error of the estimated probability for the previous problem?
(a)
0.60
(b)
0.21
(c)
0.17
(d)
0.28

13.
The probability that a car traveling along a certain road will have a flat tire is 0.05. Find the probability that among 17 cars, at least three have flat tires. Use the following information from RWEB to help answer the question.

```Rweb:> # CUMULATIVE BINOMIAL DISTRIBUTION

Rweb:> pbinom(2, 17, 0.05)

[1] 0.949747

Rweb:> # CUMULATIVE BINOMIAL DISTRIBUTION
Rweb:> pbinom(3, 17, 0.05)
[1] 0.9911994

Rweb:> # BINOMIAL PROBABILITY
Rweb:> dbinom(3, 17, 0.05)
[1] 0.04145237

Rweb:> # BINOMIAL PROBABILITY

Rweb:> dbinom(2, 17, 0.05)

[1] 0.1575190
```

(a).
0.1575
(b).
0.9497
(c).
0.0502
(d).
0.0076

14.
The cost of treatment per patient for a certain medical problem was modeled by one insurance company as a normal random variable with mean \$775 and standard deviation \$150. According to the empirical rule, what is the range of medical costs for 99.5% of the patients.

(a).
(625, 925)
(b).
(475, 1075)
(c).
(325, 1225)
(d).
(300, 600)

15.
A zero correlation between two variables, X and Y, means:
(a)
that as X increases, Y decreases.
(b)
that as X increases, Y decreases.
(c)
there is no linear relationship between X an Y.
(d)
the values of X and Y are all the same.

For the next two problems:

Four people are running for class president, Liza, Anne, Mark and Dave. The probabilities of Anne, Mark and Dave winning are 0.12, 0.27 and 0.35, respectively.

16.
What is the probability of Liza winning?

(a)
0.26
(b)
0.12
(c)
0.50
(d)
0.35

17.
What is the probability that a boy wins?
(a)
0.26
(b)
0.62
(c)
0.47
(d)
0.35

18.
Data without natural categories are called this:
(a)
sample
(b)
discrete
(c)
random
(d)
continuous

19.
Suppose we are recording temperatues for April and May in Kalamazoo. We have 61 data points which range form 40 to 84 degrees. Suppose we accidently type 840 for 84 but we enter all the other data correctly. Which of the following statistics will be dramatically affected?
(a)
Hodges-Lehmann estimate
(b)
interquartile range
(c)
median
(d)
standard deviation

20.
The probability that Bus #3 arrives on time in front of Everett Tower is 65%. What is the probability that the bus will arrive on time for 3 consecutive days? Assume that the days are independent.

(a)
0.27
(b)
0.04
(c)
1.95
(d)
0.73

Consider the following problem for the next 4 questions. Scores made by employees on a manual dexterity test are normally distributed with a mean of 600 and a variance of 10,000.

```Rweb:> # NORMAL PERCENTAGE POINT
Rweb:> qnorm(0.1,600,100)
[1] 471.8448
Rweb:> # CUMULATIVE NORMAL DISTRIBUTION
Rweb:> pnorm(300, 600, 10000)
[1] 0.4880335
Rweb:> # NORMAL PERCENTAGE POINT
Rweb:> qnorm(0.9, 600, 100)
[1] 728.1552
Rweb:> # CUMULATIVE NORMAL DISTRIBUTION
Rweb:> pnorm(300, 600, 100)
[1] 0.001349898
Rweb:> # CUMULATIVE NORMAL DISTRIBUTION
Rweb:> pnorm(850, 600, 100)
[1] 0.9937903
Rweb:> # CUMULATIVE NORMAL DISTRIBUTION
Rweb:> pnorm(700, 600, 100)
[1] 0.8413447
Rweb:> # CUMULATIVE NORMAL DISTRIBUTION
Rweb:> pnorm(450, 600, 100)
[1] 0.0668072
```

21.
What proportion of employees taking the test score below 300?.
(a).
0.0013
(b).
0.4880
(c).
0.9987
(d).
0.5120

22.
An employee is about to take the test. What is the probability that the employee's score will be 850 or more?

(a).
0.0062
(b).
0.9937
(c).
0.8413
(d).
0.0668

23.
What proportion of employees score between 450 and 700?.
(a).
0.7745
(b).
0.0039
(c).
0.0323
(d).
0.0476

24.
Management has decided that those employees whose scores are among the top 10% will be considered for promotion to a better job. What score must an employee make in order to be eligible for promotion?.

(a).
993.79
(b).
775.00
(c).
471.845
(d).
728.155

25.
Which of the following is not true about the normal distribution.

(a).
It is a distribution for continuous random variables.
(b).
The distribution has a bell shaped curve.
(c).
99.5 % of the observations fall within 3 standard deviations from the mean.
(d).
It is symmetric at its variance.