Math Answers

1. The probability distribution below shows the number of typing errors (x) and the probability p(x) of committing these errors whenever clerks type-in a document. Compute the variance and standard deviation.

y

1

2

3

4

5

P(y)

0.02

0.11

0.42

0.31

0.10

0.04

2. The probability distribution below shows the random variable and the probability of tossing a die. What is the variance and standard deviation?

z

1

2

3

4

5

6

P(z)

1/6

1/6

1/6

1/6

1/6

1/6

must include solution

The average weight of 80 randomly

selected sacks of rice is 45.54 kilos with a

standard deviation of 17 kilos. Test the

hypothesis at a 0.01 level of significance that

the true mean weight is less than 49 kilos. 2. The average length of time for students to

have their subjects controlled is 40 minutes. A

new controlling procedure using modern

computing machines is being tried. If a random

sample of 15 students has an average

controlling time of 25 minutes with a standard

deviation of 12.9 minutes under the new

system, test the hypothesis that the average

length of time to control student’s subjects is

less than 40 minutes. Use a level of

significance of 0.10 and assume the

population of controlling times to be normally

distributed.

If the weights of 600 students are normally distributed with mean of 50 kilograms and a variance of 16kilograms.

a.) Determine the percentage of students with weights lower than 55 kgs.

b.) How many students with weight between 50kgs and 55kgs.

If the weights of 600 students are normally distributed with a mean of 50 kilograms and a variance of 16 kg

b.) How many students with weights between 50 kgs and 55 kgs. (5 points)

An insurance company found that 45% of all insurance policies are terminated before their maturity date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a Binomial experiment.

a) What is the probability that eight policies are terminated before maturity?

b) What is the probability that at least eight policies are terminated before maturity?

c) What is the probability that at most eight policies are not terminated before maturity?

You are given a population of 3 elements , which are 3,4,5. Suppose all possible samples of size 2 are drawn from the population with replacement, compute for the following;

Mean of the sample means;

Variance of the sample means; and standard deviation of the sample means

A manufacturer claims that the average tensile

strength of thread A exceeds the average tensile

strength of thread B. To test this claim, 50 pieces of

each type of thread are tested under similar

conditions. Type A thread had an average of tensile

strength of 86.7 kg with a standard deviation of 6.28

kg, while type B had an average tensile strength of

77.8 with a standard deviation of 5.61 kg. Test the

manufacturer’s

claim

using

a

0.05

level

of

significance.

A group of students got the following scores in a test; 6, 9, 12, and 18. Consider samples of size 2 that can be selected from the population. What is the variance of the population?

Consider a population consisting of 2, 4, 6, 8 and 10. Suppose samples of size 3 are drawn from this population.

a. Describe the sampling distribution of the sample means

b. What are the mean and variance of the sampling distribution of the sample means? c. Construct a histogram for the sampling distribution.

Air is pumped into a spherical balloon at the rate of 100 cm3/s. How fast is the diameter increasing when the diameter is 10 cm?