Question

Consider the probability that no less than 92 out of 158 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 58%.

Approximate the probabilty using the normal distribution. Round your answer to four decimal places.

Answer 1

n=

158

p=

0.5800

here mean of distribution=μ=np=		91.64
and standard deviation σ=sqrt(np(1-p))=		6.20
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

probability that no less than 92 out of 158 students will pass their college placement exams:

probability =P(X>91.5)=P(Z>(91.5-91.64)/6.204)=P(Z>-0.02)=1-P(Z<-0.02)=1-0.492=0.5080