# Business Statistics & Probability Problems

### Description

- Complete the Chapter Review Problems (
*Statistics for Managers Using Microsoft Excel) below*:- Chapter 5, Problems 5.37, 5.39, 5.42
- Chapter 6, Problems 6.34, 6.39, 6.40

- Problem 5.37::::::Medical billing errors and fraud are on the rise. According to Medical Billing Advocates of America, three out of four times, the medical bills that they review contain errors.

Source: Kelly Gooch, Medical billing errors growing, says Medical Billing Advocates of America, Becker’s Hospital Review, website is bit.ly/2qkA8mR.

If a sample of 10 medical bills is selected, what is the probability that

0 medical bills will contain errors?

exactly 5 medical bills will contain errors?

more than 5 medical bills will contain errors?

What are the mean and standard deviation of the probability distribution? - Problem 5.39:::::: In a recent year, 46% of Google searches were one or two words, while 21% of Google searches were five or six words.

Source: Wordstream Blog, 27 Google Search Statistics You Should Know in 2019 (+ Insights!), bit.ly/2GxpUIv.

If a sample of 10 Google searches is selected, what is the probability that

more than 5 are one- or two-word searches? - Problem 5.42::::: One theory concerning the S&P 500 Index is that if it increases during the first five trading days of the year, it is likely to increase during the entire year. From 1950 through 2018, the S&P 500 Index had these early gains in 44 years (in 2011 there was virtually no change). In 36 of these 44 years, the S&P 500 Index increased for the entire year. Assuming that this indicator is a random event with no predictive value, you would expect that the indicator would be correct 50% of the time. What is the probability of the S&P 500 Index increasing in 36 or more years if the true probability of an increase in the S&P 500 Index is

0.50?

0.70?

0.90?

Based on the results of (a) through (c), what do you think is the probability that the S&P 500 Index will increase if there is an early gain in the first five trading days of the year? Explain. - Problem 6.34::::: The fill amount in 2-liter soft drink bottles is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If bottles contain less than 95% of the listed net content (1.90 liters, in this case), the manufacturer may be subject to penalty by the state office of consumer affairs. Bottles that have a net content above 2.10 liters may cause excess spillage upon opening. What proportion of the bottles will contain

between 1.90 and 2.0 liters?

between 1.90 and 2.10 liters?

below 1.90 liters or above 2.10 liters?

At least how much soft drink is contained in 99% of the bottles?

Ninety-nine percent of the bottles contain an amount that is between which two values (symmetrically distributed) around the mean? - Problem 6.39:::::The major stock market indexes had weak results in 2018. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was ?6.24%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was ?3.88%. Historically, the one-year returns are approximately normally distributed, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the NASDAQ is approximately 30%.

What is the probability that a stock in the S&P 500 gained value in 2018?

What is the probability that a stock in the S&P 500 gained 10% or more in 2018?

What is the probability that a stock in the S&P 500 lost 20% or more in 2018?

What is the probability that a stock in the S&P 500 lost 30% or more in 2018?

Repeat (a) through (d) for a stock in the NASDAQ.

Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation. - Problem 6.40::::: Interns report that when deciding on where to work, career growth, salary and compensation, location and commute, and company culture and values are important factors to them. According to reports by interns to Glassdoor, the mean monthly pay of interns at Intel is $5,940.

Source: Data extracted from www.glassdoor.com/index.htm.

Suppose that the intern monthly pay is normally distributed, with a standard deviation of $400. What is the probability that the monthly pay of an intern at Intel is

less than $5,900?

between $5,700 and $6,100?

above $6,500?

Ninety-nine percent of the intern monthly pays are higher than what value?

Ninety-five percent of the intern monthly pays are between what two values, symmetrically distributed around the mean?