Given a population in which the probability of a success is p = 0.40, if a sample of 1,000 is taken,

a. Calculate the probability the proportion of successes in the sample will be less than 0.42.

b. What is the probability the proportion of successes in the sample will be greater than 0.44?

7-52. A random sample of size 100 is to be taken from a population that has a proportion equal to 0.35. The sample proportion will be used to estimate the population proportion.

a. Calculate the probability that the sample proportion will be within {0.05 of the population proportion.

b. Calculate the probability that the sample proportion will be within {1 standard error of the population proportion.

c. Calculate the probability that the sample proportion will be within {0.10 of the population proportion.