Answer:
The standard deviation of the number of people who believe that the product is in fact improved is 1.50.
Explanation:
The random variable X can be defined as the number of people who believe that a product is improved when they are told so.
The probability of a person believing that a product is improved is, p = 0.25.
A random sample of n = 8 people who are given a sales talk about a new, improved product are selected.
The event of a person believing that the product is improved is independent of others.
The random variable X follows a Binomial distribution with parameters n = 8 and p = 0.25.
The success is defined as a person believing that a product is improved.
The mean and standard deviation of a Binomial distribution is given by:
μ = n × p
σ = √[n × p × (1 - p)]
Compute the standard deviation as follows:
σ = √[n × p × (1 - p)]
= √[8 × 0.25 × (1 - 0.25)]
= √(2.25)
= 1.50
Thus, the standard deviation of the number of people who believe that the product is in fact improved is 1.50.