Question

Let x be binomial random variable with n=50 and p=.3. The probability of less than or equal to 13 successes, when using the normal approximation for binomial is ________. (Please show how to work the problem).

a) -.6172

b) .3086

c) 3.240

d) .2324

e) .2676

f) -.23224

Answer 1

Solution :

Given that,

p = 0.3

q = 1 - p = 1 - 0.3 = 0.7

n = 50

Using binomial distribution,

Mean = = n * p = 50 * 0.3 = 15

Standard deviation = = n * p * q = 50 * 0.3 * 0.7 = 3.24

P(x < 13) = P[(x - ) / < (13 - 15) / 3.24 ]

= P(z < -0.62)

Using z table,

= 0.2676

correct option is = e