BIOSTATISTIC

1.Given the probability distribution

X

8

15

16

24

P(X=x)

1/4

1/3

3/8

1/6

Find the expected value of X2or E(x2)

select one

a.253

b.283

c.273

d.263

2.In a company-sponsored contest, the chance of winning various amounts of money is given here:

Price (Dollar)

500

100

50

1

0

Win Probability

0.01

0.03

0.11

0.50

0.35

What is the expected value and standard deviation of the price?

Select one:

a.14,53.66

b.130.2, 14

c.14, 42.42

d.53.66, 14

e.53.66, 130.2

3.You are given a very largenormal distributionwith a = 200 and = 85. A sample of 500 is drawn from the population. How many would you expect to have values between 150 and 250? Let the = np

Select one:

a.372

b.361

c.222

d.139

e.0.7224

4.Two hundred college junior have their grades in thenormal distributionwith a mean of 2.2 and a standard deviationof 0.6. How many of these junior have their grades between 2.0 and 2.5 inclusive?

Select one:

a.0.4818

b.56

c.76

d.0.2818

e.0.5818

5.Which of the following are true about thenormal distribution?

I. The total area under the standard normal curve is equal to 1.

II. The total area under a nonstandard normal curve is equal to 1.

III. Everynormal distributioncan be standardized.

Select one:

a.I and III only

b.I only

c.I, II and III

d.III only

e.I and II only

6.A lot of 100 batteries is known to certain 10 defective batteries. Five batteries are selected at random and each battery is replaced before the next battery is selected. What is the battery of getting at most two defective batteries?

Select one:

a.0.32805

b.0.99144

c.0.59049

d.0.89412

e.0.0729

7.For the probability distribution given below, find the mean.

X

-10

-20

30

P(X=x)

1/5

3/10

Select one:

a.7

b.8

c.5

d.6

8.A production of 20 fuses is received by the store. It is known that 4 of the fuses are defective. The quality-control engineer randomly selected three of the fuses from the production run. Find the probability that two of the fuses selected are defective.

Select one:

a.0.6415

b.0.08421

c.0.1587

d.0.3245

e.0.6588

9.If approximately, 1 % of the people in a certain compound of 200 people left-handed, find the probability that exactly five people are left-handed.

Select one:

a.0.0999

b.0.00015

c.0.1464

d.0.0360

e.0.0183

10.Which of the following statements is true for anormal distribution?

Select one:

a.It goes to infinity in both directions

b.It has two parameters: a mean and a standard deviation

c.All of the above

d.Half of the values are greater than the mean.

11.Jack scored 82 on a test in which = 76 and = 7. Jill scored 85 on a test in which = 78 and = 8. If both sets of scores are normally distributed, who score better on their test relative to the rest of the class?

Select one:

a.Jack, since the standard deviation was smaller

b.Jack, since his z-score was higher

c.Jill, since her z-score was higher

d.Jill, since the standard deviation is greater

e.Cannot tell since the distribution are not compatible

12.What is the probability that a randomly selected member of a normally distributed population will lie more than 1.8 standard deviations from the mean?

Select one:

a.0.9641

b.0.1841

c.0.8159

d.0.0718

e.0.0359

13.Records in the city of General Trias, shows that the average number of stores closing in a year due to loss is 2. What is the probability that there will be 4 stores closing this year because of loss?

Select one:

a.0.2240

b.0.1464

c.0.090

d.0.0360

e.0.0183

14.A lottery has one prize of Php 100,000, two prizes of Php 50,000, five prizes of Php 25,000 and ten prizes of Php 10,000. If there are 100,000 tickets sold, what is the expected value of a ticket?

Select one:

a.Php 4.00

b.Php 4.75

c.Php 4.25

d.Php 4.50

15.A telephone operator receives3 calls per hour. Find the probability it will receive four or more calls.

Select one:

a.0.6472

b.0.3528

c.0.2240

d.0.0498

e.0.1494

16.Suppose that in an examination, the cut-off score for passing is 75 for 200 people. If the mean of the test is 84 with a standard deviation of 5 and the scores are normally distributed, what proportion of people passed the test?

Select one:

a.0.4641

b.0.

0.9641

c.189

d.193

e.0.2881

17.Find the probability that ina family of three children there will be at least 1 boy and 1 girl.

Select one:

a.1/4

b.7/8

c.3/8

d.1/8

e.3/4

18.Which of the following are true about thenormal distribution?

I. The standard deviation get smaller as z increases.

II. Approximately 68% of the area under a normal curve lie within one variance of the mean.

III. Normal distributions are asymmetric about the mean.

Select one:

a.I and II

b.All of the statements are true

c.II and III

d.None of the statement is true

e.I and III

19.Which of the following investments gives you the best opportunity to make money ( highest expected value)?

Investment A: You have a 20% chance of making 50,000 and a 80% chance of losing your 8,000 investment.

Investment B: You have a 10% chance of making 100,000 and a 90% chance of losing your 8,000 investment.

Investment C: You have a 40% chance of making 30,000 anda 60% chance of losing your 14,000 investment.

Select one:

a.Either B or C, but not A

b.The expected value is different for each investment

c.Either A or B, but not C

d.All three investments have a negative expected value

e.Either A or C, but not B

20.An average of 2 cars arrive at a highway tollgate every 10 seconds. If this rate is approximated, what is the probability that exactly 3 cars will arrive in a 10 seconds period?

Select one:

a.0.14902

b.0.01492

c.0.82563

d.0.18040

e.0.00113

21.Records show that the probability a tire will suffer a blowout in the next year is 0.001. If 200 tires are used for a year, what is the probability of exactly 3 blowouts?

Select one:

a.0.32456

b.0.41257

c.0.0011

d.0.1804

e.0.00224

22.A sample of 150 students was considered with a mean weight of 65 kilos and the standard deviationof 5 kilos. Find how many many students weigh between 60 and 70 kilos. Let the = np.

Select one:

a.0.7286

b.0.7041

c.109

d.0.0668

e.10

23.The probability function, g(x) = 0.02x is defined for x = 8, 9, 10, 11, and 12. What is the mean of this probability distribution?

Select one:

a.20

b.This is not a probability distribution?

c.10.2

d.50

e.10

24.Find the area under the standardnormal distributioncurve between z = - 0.03 and 0.53.

Select one:

a.0.2139

b.0.9131

c.0.0233

d.0.8284

e.0.8329

25.Find theprobability that in tossing a fair coin three times there will appear 2 heads and 1 tail.

Select one:

a.3/8

b.1/2

c.3/4

d.1/8

e.1/4

26.Six cards are drawn from a deck of 52 well- shuffled cards. Find the probability that are any of one suit and 3 are ofanother.

Select one:

a.323 / 2,049

b.512 / 2, 544,815

c.2 / 2,544,815

d.3 / 54,145

e.9,438 / 195,755

27.A faculty student committee is to be selected at random from three students and 4 faculty members. The committee is to consist of two persons. Find the probability that the committee will contain 2 students.

Select one:

a.3/7

b.4/7

c.6/7

d.2/7

e.1/7

28.Find the area under the standardnormal distributioncurve between z = 1.32 and 1.82.

Select one:

a.0.8329

b.0.4744

c.0.0590

d.0.2139

e.0.1443

29.Which of the following events are true?

I. The standard deviation of arandom variableis always positive.

II. The variance of arandom variableis always greater than the standarddeviation.

III. The law of large numbers implies that as a probability experiment is repeated, the variance will approach to zero.

Select one:

a.II only

b.II and III

c.I and II

d.I only

e.None of the above statements is true

30.Which of the following are true about thenormal distribution?

I. It is symmetric about the mean; the mean, median and mode are all the same; more than

90% of the distribution is within 2 standard deviations of the mean.

II. The normal density curve is defined by its mean and standard deviation and nothing else; there is no largest or smallest data value.

III. An interval x units and centered about the mean represents more data values than any other interval x units wide.

Select one:

a.I and II

b.II and III

c.I only

d.I and III

e.I, II and III