Question

Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 24.0 percent of the respondents. Estimate the probability that among the next 166 responses there will be at most 43 correct answers.

SELECT ALL APPLICABLE CHOICES

A) 74.56870%

B) 74.30203%

C) 75.20203%

D) 74.95203%

E) 74.70203%

F) None of the above

Answer 1

Binomial to normal approximations with continuity factor

Sample size , n =    166                      
Probability of an event of interest, p =   0.24                      
left tailed                          
X ≤    43                      
                          
Mean = np =    39.84                      
std dev ,σ=√np(1-p)=   5.5026                      
                          
P(X ≤   43   ) = P(Xnormal ≤   43.5   )          
                          
Z=(Xnormal - µ ) / σ = (   43.5   -   39.84   ) /   5.5026   =   0.665
                          
=P(Z≤   0.665   ) =    0.7470203              
so, answer: 74.70203%