Final answer:
The parameter we want to estimate is the proportion of sales coming from online shopping. The value of the parameter is 65% and the point estimate based on this survey is 68%. The probability distribution used to determine the probabilities of this sample proportion is the binomial distribution. The mean of this distribution is 48.75 and the standard error is 3.858. The probability that in a sample of 75 sales, at least 60 of them were from online shopping is 0.9024.
Step-by-step explanation:
a) The parameter we want to estimate is the proportion of sales coming from online shopping. The value of the parameter is 65% (given) and the point estimate based on this survey is 51/75 = 0.68 or 68%.
b) The probability distribution that will be used to determine the probabilities of this particular sample proportion is the binomial distribution. This is because we are dealing with a fixed number of trials (75 sales) with only two possible outcomes (online shopping or not online shopping) and each trial has the same probability of success (65% or 0.65).
c) The mean of this distribution is obtained by multiplying the sample size (75) by the probability of success (0.65), so the mean is 75 * 0.65 = 48.75. The standard error of this distribution is the square root of (n * p * (1 - p)), so the standard error is sqrt(75 * 0.65 * (1 - 0.65)) = 3.858.
d) To calculate the probability that in a sample of 75 sales, at least 60 of them were from online shopping, you can use the following excel formula: =1-BINOM.DIST(59,75,0.65,TRUE) = 0.9024