Question

Assume a binomial probability distribution with n=55n=55 and π=0.34π=0.34 . Compute the following: (Round all your z values to 2 decimal places.)

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

PLEASE:(

2. The probability that X is 22 or more. (Use the rounded values found above. Round your answer to 4 decimal places.)

3. The probability that X is 14 or less. (Use the rounded values found above. Round your answer to 4 decimal places.)

Answer 1

a)

Mean = n * = 55 * 0.34 = 18.7

Standard deviation = sqrt [ n * * ( 1 - ) ]

= sqrt [ 55 * 0.34 ( 1 - 0.34) ]

= 3.5131

b)

Using normal approximation

P(X < x) = P(Z < (x - Mean) / SD)

So,

P(X >= 22) = P(Z > (21.5 - 18.7) / 3.5131) [ With continuity correction ]

= P(Z > 0.80)

= 0.2119

c)

P(X <= 14) = P( Z < ( 14.5 - 18.7) / 3.5131) [ With continuity correction ]

= P(Z < -1.20)

= 0.1151