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  

=>  

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

126 maybe. sorry