State whether the following statements are True or False Mea

State whether the following statements are True or False.

Mean value over an infinite number of observations of the variables is the expected value of a random variables.

A standard normal distribution has the mean equal to the variance.

Data that are influenced by many small and unrelated random effects are approximately normally distributed.

A critical value is a z score separating unlikely values from those that are likely to occur.

It is 90% (or 0.90) confidence level for corresponding value of = 0.20

...........................................................................

(Multiple Choice Questions)   

Which one of these variables is a continuous random variable?

The time it take a randomly selected student to complete an exam

The number of children in a family

The number of women taller than 68 inches in a random sample of 5 women.

The number of correct guesses an a multiple choice test.

Selection of favorite fruits and responses of orange, grape, apple, kiwi or other many were recorded are

Probability distribution

Binomial distribution

Poisson distribution

none

.............................................................

Which of the following is NOT a possible probability?

25/100

1.25

1

0

...............................................

If the z – score of normal distribution is 2.5, the mean of the distribution is 45 and the standard deviation of normal distribution is 3 then the value of X for a normal distribution is

97.5  

47.5  

52.5

67.5

..............................................

5. If the sampling error (E) is allowed to increase, which of the following is true regarding the sample size?

The sample size will increase

The sample size will decrease

The sample size will stay the same

The sample size cannot be determined

.....................................................................

Answer the following Essay Type Questions   

During the summer months, a rental agency keeps track of the number of chain saws it rents each day during a given period and X denotes the number of saws rented per day. Describe a probability distribution, if it is probability distribution, find the mean, variance, and standard deviation for the probability distribution.

.....................................................................

If X is binomially distributed with 6 trials and a probability of success equal to ¼ at each attempt. What is the probability of exactly 4 success? Also find the parameter mean, variance and standard deviation.

Find

        a) P(z < 2.37)

b) P(z > 1.82)

c) P(-1.18 < z < 2.1)

x	0	1	2
p(x)	0.5	0.33	0.17

Solution

Mean value over an infinite number of observations of the variables is the expected value of a random variables.- true
A standard normal distribution has the mean equal to the variance. - false
Data that are influenced by many small and unrelated random effects are approximately normally distributed. - true
A critical value is a z score separating unlikely values from those that are likely to occur.- true
It is 90% (or 0.90) confidence level for corresponding value of = 0.20 - false

MCQ

1.The number of women taller than 68 inches in a random sample of 5 women

2.Binomial distribution

3.1,25

4.67.5

5.The sample size will stay the same