Question

Seven customers enter a clothing store and are observed to determine if they will make a purchase. The store owner states that there is a 75% chance of a customer making a purchase. The random variable x represents a customer making a purchase. Calculate the mean, variance and standard deviation for the number of customers that make a purchase.

Answer 1

Answer: Mean = 5.25

Variance = 1.3125

Standard deviation = 1.456

Explanation:

The mean and variance of a binomial distribution with parameters n (number of trials) and p ( the probability of getting success in each trial) is given by :-

`\text{Mean}=np\\\\\text{Variance}=np(1-p)`

Given : The total number of enter a clothing store : n=7

The probability of a customer making a purchase= 0.75

Now,

`\text{Mean}=7(0.75)=5.25\\\\\text{Variance}=7(0.75)(0.25)=1.3125\\\\\Rightarrow\ \text{Standard deviation}=√(1.3125)=1.14564392374\approx1.1456`