Free Printable SM025 SPECIAL PROBABILITY DISTRIBUTIONS

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SM025 SPECIAL PROBABILITY DISTRIBUTIONS

Total questions: 50

Worksheet time: 3hrs 30mins

Name

Class

Date

Choose the correct sign for

'probability when X is greater than 4 and at most 9'

$P(4<X<9)$

$P(4<X\le9)$

$P(4\le X\le9)$

$P(4\le X<9)$

Find the standard deviation of a binomial distribution with $n=50$ and $p=0.4$ . Give your answer in 2 decimal places.

(a)

If $X\sim Po(1.8)$ , find $P(2\le X\le4)$ . Give your answer to 4 decimal places.

(a)

A shop sells radios at a rate of 2.5 per week.

Find the probability that in a two-week period the shop sells at least 7 radios.

Give your answer to 4 decimal places.

(a)

The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What proportion of weeks would you expect to have less than 5 accidents? Give your answer to 4 decimal places.

(a)

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 68?

420.65

421

250

Assuming that a normal distribution is a reasonable approximation for a binomial distribution, what value is used to approximate the mean?

$nq$

$np$

$\frac{n}{p}$

$\frac{n}{q}$

Assuming that a normal distribution is a reasonable approximation for a binomial distribution, what value is used to approximate the standard deviation?

$npq$

$np$

$\sqrt[]{np}$

$\sqrt[]{npq}$

Perform continuity correction for $P(X\ge4)$

$P(X=4.5)$

$P(X>5.5)$

$P\left(X\ge3.5\right)$

$P(X>4.5)$

10.

Perform continuity correction for at most 20

$P(X>20.5)$

$P\left(X\le20.5\right)$

$P(X>19.5)$

$P(X<19.5)$

11.

30% of all cats in a city are micro-chipped. In a sample of 500 cats, what is the probability that less than 140 cats are micro-chipped? Select the closest option.

0.25

0.21

0.17

0.13

12.

In a survey it was found out that 20% of all working people exercise everyday. A sample of 10 working people was taken. Find the probability that 1 to 5 of them exercise everyday.

0.8862

0.9276

0.7456

0.8772

13.

The probability that a machine will break down in a day is 0.1. Out of 30 days, find the probability that the machine will break down at most 4 times

0.8798

0.9001

0.7542

0.8245

14.

It was found that 2% of the pens supplied by a company have defects. Find the probability that in a box that contains 150 pens, 8 pens have defects.

0.0249

0.0076

0.1265

0.0054

15.

A department store sells an average 3 electrical appliances per day. Assume the sale is a Poisson distribution. Find the probability that on a given week this store will sell exactly 6 electrical appliances.

0.9999

0.0001

0.8992

0.0012

16.

An average of six telephone calls are received by a department every hour. Find the probability that 2 to 4 calls are received per 20 minutes

0.1339

0.0766

0.5940

0.5413

17.

In a library, the mean of the number of students borrowing book between 8.00pm and 8.40pm is 8. Find the probability that at least one student borrows books in the first 15 minutes.

0.8446

0.9502

0.3023

0.5670

18.

The life span of a calculator has a normal distribution with a mean of 60 months and a standard deviation of 5 months. A calculator that starts malfunctioning within $4\frac{1}{6}$ years of the purchase will be replaced by a new one. Find the percentage of calculators that are expected to be replaced.

2.28

0.0228

0.00228

0.2280

19.

It was observed that 25% of those contacted personally by a sales representative will make a purchase. If a sales representative contacts 40 prospects, find the probability that 20 or more will make a purchase.

0.0567

0.00026

0.4562

0.50063

20.

80% of the books in a cupboard are academic books. If there are 50 books in the cupboard, find the probability that 40 books taken at random from the cupboard are academic books, by using the normal distribution to approximate binomial distribution.

0.1673

0.1126

0.1406

0.1398

21.

Which of the following is NOT an assumption of the Binomial distribution?

All trials must be independent.

Each trial must be classified as a success or a failure.

All trials are dependent on each other.

The number of successes in the trials is counted.

22.

The mean number of accidents per month at a certain intersection is 3.What is the probability that in any given month exactly 4 accidents will occur at this intersection?

0.081

0.672

0.168

0.750

23.

Choose the correct sign

'probability at most 7'

P(X>7)

P(X<7)

P(X≥7)

P(X≤7)

24.

The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inches. If waist sizes are normally distributed, find the probability of teenagers with waist sizes greater than 31 inches.

0.924

0.105

0.160

0.076

25.

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has Type B blood?

0.088

0.697

0.214

0.303

26.

The marks obtained by the students are normally distributed with mean 61 marks and variance 100 marks. Find the probability of the students obtain at least 85 marks.

0.4207

0.0082

0.1112

0.9918

27.

Assuming that breakdowns in electricity supply occur ramdomly with mean of one breakdown every 10 weeks. Find the probability of at least 2 breakdowns in any period of one week

0.0047

0.0952

0.0002

1.000

28.

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.

Find the percentage of golfers that are between 30 and 46 years old.

68%

94%

95%

99.7%

29.

What is the the total area under the standard normal distribution curve?

100

0.5

1.0

30.

An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct?

0.962

0.132

0.831

0.250

31.

A company states that 2% of its computers are returned for defects. We take a sample of 100 computers to find the probability of 10 being defective. Is this a binomial distribution?

No because there is not a fixed number of trials.

No because their are more than 2 outcomes.

Yes since there are a fixed number of independent trials, outcomes in 2 categories, and the probability of defect is constant.

No since computers would not be independent.

32.

Which of the following is not true of the normal distribution

The curve is bell shape

The curve approaches the x-axis gradually on either side of the mean

The distribution is symmetrical about the vertical line drawn from the peak of the curve

The curve is symmetrical

33.

Which of the following is NOT an assumption of the Binomial distribution?

All trials must be independent.

Each trial must be classified as a success or a failure.

All trials are dependent on each other.

The number of successes in the trials is counted.

34.

Which of the following is false about binomial probabilities?

Their distributions are approximately symmetric.

Trials must be fixed.

Events musts be independent.

The probability of success must be 0.50

35.

X ~ B(20, 0.5)

Find P(X = 7)

0.07

0.13

0.87

0.94

36.

X ~ B(20, 0.5)

Find P(X ≤ 7)

0.07

0.13

0.87

0.94

37.

X ~ B(20, 0.5)

Find P(X ≥ 7)

0.07

0.13

0.87

0.94

38.

X is the number of heads when a fair coin is flipped 12 times

Find P(X = 4)

0.12

0.19

0.81

0.93

39.

Poisson is a __________ probability distribution

random

discrete

continuous

40.

What is the parameter of Poisson distribution?

$\mu$

$\sigma$

$\lambda$

41.

Poisson distribution expresses the probability of events occurring in a fixed interval of _______ or _______.

time, distance

time, space

distance, space

42.

If the mean of a Poisson distribution is 4,what is its variance?

43.

Poisson Formula: P(X=x)

44.

Which of the following is the correct formula to find the expected value of any Poisson random variable "x"?

$E\left(x\right)=\lambda$

$E\left(x\right)=e\cdot\lambda$

$E\left(x\right)=\lambda^2$

$E\left(x\right)=e$

45.

Which of the following is the correct formula to find the variance of any Poisson random variable "x"?

$Var\left(X\right)=\lambda$

$Var\left(X\right)=e\cdot\lambda$

$Var\left(X\right)=\lambda^2$

$Var\left(X\right)=e$

46.

The width of the curve is determined by the _____________________.

Mean

Variation

Standard Deviation

Standard Normal Curve

47.

A standard normal curve is a normal probability distribution that has a standard deviation of ____ and a mean of ____.

1, 0

0, 1

0, 0

1, 1

48.

What is the formula to find the corresponding z-score for population data?

z = X - μ / σ

z = (X - μ) / σ

z = μ - X / σ

z = (μ - X) / σ

49.

Which of the following is NOT TRUE?

The mean, median, and the mode are equal.

The curve is asymptotic to the base line.

The total area under the curve is less than 1.

The curve is symmetrical about its center.

50.

Which is NOT a characteristic of normal distribution?

Symmetrical

Bell-shaped

Random

Continuous

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SM025 SPECIAL PROBABILITY DISTRIBUTIONS

Total questions: 50

Worksheet time: 3hrs 30mins

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