Given a population where the probability of success is p= 0.40, calculate the probabilities below if a sample of is taken. Calculate the probability the proportion of successes in the sample will be . What is the probability the proportion of successes in the sample will be ?

Complete Question

Given a population where the probability of success is  p= 0.40 calculate the probabilities below if a sample of 300 is taken.

A. Calculate the probability the proportion of successes in the sample will be less than 0.42 (round 4 decimals)

B. What is the probability that the proportion of successes in the sample will be greater than 0.44 (round 4 decimals)

A

B

Step-by-step explanation:

From the question we are told that

       The  probability of success is  p =  0.40

       The sample size is  n  =  300

Generally given that the sample size is large enough n  > 30  then the mean for this sampling distribution is  

Generally the standard deviation is mathematically represented as

=>    

=>      

Considering question A  

Generally the probability the proportion of successes in the sample will be less than 0.42 is mathematically represented as

=>  

From the z table  

  The area under the normal  curve  to the left corresponding to 0.7072 is  

=>  

Considering question B  

Generally the probability the proportion of successes in the sample will be less than 0.44 is mathematically represented as

=>  

From the z table  

  The area under the normal  curve  to the left corresponding to 1.4144 is  

=>  

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.