The Wall Street Journal reported that approximately 25% of the people who are told a product is improved will believe that it is in fact improved. The remaining 75% believe that this is just hype. Suppose a marketing study consists of a random sample of eight people who are given a sales talk about a new, improved product. What is the standard deviation of the number of people who believe that the product is in fact improved

The standard deviation of the number of people who believe that the product is in fact improved is 1.50.

Step-by-step 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.