Question

the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016.In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016.

Answer 1

Using the binomial distribution, the mean and the standard deviation for the number of settled complaints among those received are given as follows:

• Mean: 160 complaints.

• Standard deviation: 5.66 complaints.

What are the mean and the standard deviation for the binomial distribution?

The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial. These parameters will be used to find the mean and the standard deviation, with formulas that are presented next.

The mean is given as follows:

$E(X) = np$

The standard deviation is given as follows:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Considering that a sample of 200 complains are chosen, each with an 90% probability of being settled, the parameters are given as follows:

n = 200, p = 0.8.

Hence the mean is:

$E(X) = np = 200 \times 0.8 = 160$

The standard deviation is:

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200 \times 0.8 \times 0.2} = 5.66$

What is the missing information?

The problem states that 200 complaints were received, and asks for the mean and the standard deviation for the number of settled complaints among those received.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1