Question

If np greater than or equals 5 and nq greater than or equals 5, estimate Upper (fewer than 5) with n =14 and

p = 0.6 by using the normal distribution as an approximation to the binomial distribution; if np less than 5 or nqless than 5, then state that the normal approximation is not suitable.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. P(fewer than 5) = ____

(Round to four decimal places as needed.)

B.

The normal approximation is not suitable.

Answer 1

Solution :

Given that,

p = 0.6

q = 1 - p = 1 - 0.6

n = 14

np = 14 * 0.6 = 8.4 > 5

nq = 14 * 0.4 = 5.6 > 5

The normal approximation is suitable .

Using binomial distribution,

= n * p = 14 * 0.6 = 8.4

= n * p * q = 14 * 0.6 * 0.4 = 1.833

Using continuity correction ,

P(x < 4.5) = P((x - ) / < (4.5 - 8.4) / 1.833)

= P(z < -2.13)

= 0.0166

Probability = 0.0166