The daily sales at a convenience store have a mean of $1350 and a standard deviation of $150. The mean of the sampling distribution of the mean sales of a sample of 25 days for this convenience store is:

The mean of the sampling distribution = $1350

Step-by-step explanation:

Given -

Population mean = $1350

Standard deviation = $150

Sample size ( n ) = 25

The mean of the sampling distribution = population mean

The mean of the sampling distribution = $1350

0.021739

Step-by-step explanation:

This situation can be modeled with the Binomial Distribution which gives the probability of an event that occurs exactly k times out of n, and is given by

where  

= combination of n elements taken k at a time.

p = probability that the event (“success”) occurs once

q = 1-p

In this case, the event “success” is winning the roulette game with probability 1/36 = 0.027777 and n=100 rounds.

The probability value of winning the roulette game 7 or more times out of 100, is  

P(7;100)+P(8;100)+...+P(100;100) =

1 - P(0;100)+P(1;100)+...+P(6;100)

We can find the sum of these last 7 terms either by hand or computer-assisted and we would find  

P(0;100)+P(1;100)+...+P(6;100) =

and  the p-value (probability value) for winning 7 or more out of 100 rounds is

1-0.978261 = 0.021739