A random sample of size n = 60 is selected from a binomial distribution with population proportion p = 0.25.
(a) What will be the approximate shape of the sampling distribution of p?
(b) What will be the mean and standard deviation (or standard error) of the sampling distribution of p?? (Round your answers to four decimal places.)
(c) Find the probability that the sample proportion p? is strictly between 0.13 and 0.47. (Round your answer to four decimal places.)

a)

With the following parameters:

b)

c)

And for this case we can use the following difference and the normal standard distribution table or excel and we got:

Step-by-step explanation:

For this case we have the following info:

n = 60 represent the sample size

p = 0.25 represent the proportion of success

For this case we can check the conditions to use the normal distribution:

1) np= 60*0.25=15>10

2) n(1-p)= 60(1-0.25) = 45>10

So then we can use the normal distribution as an approximate distribution for p

Part a

Part b

With the following parameters:

Part c

For this case we want this probability:

And for this case we can use the z score given by:

And using this formula we got:

And for this case we can use the following difference and the normal standard distribution table or excel and we got:

the answer is c.

step-by-step explanation: