Question

Use the normal approximation to the binomial to find the probability for n 52,p 0.7, and X s40. Roundz-value calculations to 2 decimal places and final answer to 4 decimal places. The probability is 0.8951 -]

Answer 1

X has mean = n*p = 52*0.7 = 36.4

and variance = n*p*(1-p) = 52*0.7*0.3 = 10.92

Using continuity correction of 0.5 (discrete random variable modeled by a continuous discretion),

P( X <= 40 ) = P( X <= 40.5 )

$= P( \frac{X-\mu}{\sigma} \leq \frac{40.5 - 36.4}{\sqrt{10.92}}) = P(Z \leq 1.2407) = 0.8926$