In a binomial experiment, find the probability of between 33 and 38 successes in 150 trials if . Round your answer to four decimal places.
A) 0.2641
B) 0.7359
C) 0.1321
D) 0.3962
E) 0.0660

Question

In a binomial experiment, find the probability of between 33 and 38 successes in 150 trials if  . Round your answer to four decimal places. ​
A) 0.2641 
B) 0.7359 
C) 0.1321 
D) 0.3962 
E) 0.0660

Quizplus · Accepted Answer

We can use the normal approximation to the binomial distribution using the following formula:

μ = np 
σ = sqrt(np(1-p))

where n=150, p=11/984, μ = mean and σ = standard deviation

μ = 150 × 11/984 ≈ 1.686 
σ = sqrt(150 × 11/984 × (1-11/984)) ≈ 1.124

We can convert the given range of values to standard units as follows:

z1 = (33-μ)/σ ≈ 30.13 
z2 = (38-μ)/σ ≈ 34.06

Using a standard normal distribution table, we can find the area between these two values to be approximately 0.2641. Therefore, the probability of between 33 and 38 successes in 150 trials is 0.2641.

In a Binomial Experiment, Find the Probability of Between 33