Question

Assume a binomial probability distribution with n= 45 and π= 0.28 . Compute the following: (Round all your z values to 2 decimal places.)

A. The mean and standard deviation of the random variable. (Round your "σ" to 4 decimal places and mean to 1 decimal place.)

B. The probability that X is 17 or more. (Use the rounded values found above. Round your answer to 4 decimal places.) ​​

C. The probability that X is 7 or less. (Use the rounded values found above. Round your answer to 4 decimal places.)

Answer 1

Random variable X follows Binomial distribution with n = 45 and

> 10

So we can use here normal approximation with mean and standard deviation given below:

A) Mean =

          = 45 * 0.28

          = 12.6

Mean = 12.6

Standard deviation

= 3.0120             (Round to 4 decimal)

Standard deviation = 3.0120

Define new random variable Y follows Normal with mean = and standard deviation =

Since Binomial is discrete and normal is continuous , a continuity correction factor must be applied when using normal approximation to binomial distribution. In general, following adjustments are made for finding probabilities:

Exact Binomial probability	Normal Approximation

B) Here we have to find

                         

                         

                                    Where z is standard normal variable

                                                      (Round z to 2 decimal)

                          = 1 - P(z < 1.29)

                          = 1 - 0.9015                   (From statistical table of z values)

                          = 0.0985

C) Here we have to find

                      

                      

                      

                                    (Round z to 2 decimal)

                       = 0.0455