1 If the z score of normal distribution is 25 the mean of t

1. 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 [with steps]

a) 97.5  

b) 47.5  

c) 52.5

d) 67.5

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

a. Probability distribution

b. Binomial distribution

c. Poisson distribution

d. none

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

a) The sample size will increase

b) The sample size will decrease

c) The sample size will stay the same

d) The sample size cannot be determined

Q/ 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)

Q/ 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.

Solution

I.
Normal Distribution
Mean ( u ) =45
Standard Deviation ( sd )=3
Normal Distribution = Z = X- u / sd ~ N(0,1)                  
2.5 = ( X - 45 )/3

X - 45 = 7.5
X = 52.5

II.
a. Probability distribution

III.
b) The sample size will decrease

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