Data Analytics

Question # 223 - According to data from the National Health and Nutrition Examination Survey, 33% of white, 49.6% of black, 43% of Hispanic, and 8.9% of Asian women are obese. In a representative town, 48% of women are white, 19% are black, 26% are Hispanic, and the remaining 7% are Asian.

a. Find the probability that a randomly selected woman in this town is obese.

b. Given that a woman is obese, what is the probability that she is white?

c. Given that a woman is obese, what is the probability that she is black?

d. Given that a woman is obese, what is the probability that she is Asian?

Question # 224 - Brad Williams, owner of a car dealership in Chicago, decides to construct an incentive compensation program based on performance.

Calculate the expected value of the annual bonus amount.

Calculate the variance and standard deviation of the annual bonus amount.

Question # 332 - A hospital administrator worries about the possible loss of electric power as a result of a power blackout. The hospital, of course, has a standby generator, but it, too, is subject to failure, having a mean time between failures of 500 hours. It is reasonable to assume that the time between failures is exponentially distributed.

a. What is the probability that the standby generator fails during the next 24-hour blackout?

b. Suppose the hospital owns two standby generators that work independently of one another. What is the probability that both generators fail during the next 24-hour blackout?

Question # 226 - Akiko Hamaguchi, manager of a small sushi restaurant, Little Ginza, in Phoenix, Arizona, has to estimate the daily amount of salmon needed.

Akiko has estimated the daily consumption of salmon to be normally distributed with a mean of 12 pounds and a standard deviation of 3.2 pounds.

Buying 20 lbs of salmon every day has resulted in too much wastage.

Therefore, Akiko will buy salmon that meets the daily demand of customers on 90% of the days.

Based on this information, Akiko would like to:

Calculate the proportion of days that demand for salmon at Little Ginza was above her earlier purchase of 20 pounds.

Calculate the proportion of days that demand for salmon at Little Ginza was below 15 pounds.

Determine the amount of salmon that should be bought daily so that it meets demand on 90% of the days

Paper Use Each American uses an average of 650 pounds of paper in a year. Suppose that the distribution is approximately normal with a population standard deviation of 153.5 pounds. Assume the variable is normally distributed. Find the probability that a randomly selected American use

a. More than 800 pounds of paper in a year

b. Less than 400 pounds a year

c. Between 500 and 700 pounds a year.

Question # 336 - The data table MV Houses shows a portion of the sale price (in $1,000s) for 36 homes sold in Mission Viejo, CA, during June 2010.

a. Summarize range of house prices

b. Comment on where house prices tend to cluster.

c. Calculate percentages to compare house prices

Question # 338 - A manager of a local retail store analyzes the relationship between advertising (in $100s) and sales (in $1000s) by reviewing the store’s data for the previous 6 months.

a. Calculate the mean of advertising and the mean of sales.

b. Calculate the standard deviation of advertising and the standard deviation of sales.

c. Calculate and interpret the covariance between advertising and sales.

d. Calculate and interpret the correlation coefficient.

Question # 440 - Butterfly wings: Do larger butterflies live longer? The wingspan (in millimeters) and the lifespan in the adult state (in days) were measured for 22 species of butterfly. Following are the results.

1. Construct a scatterplot of the lifespan (y) versus the wingspan (x).

2. Compute the correlation coefficient between wingspan and lifespan.

Question # 552 - The following data represents the overall miles per gallon (MPG) of 2014 midsized sedans:

(a) Compute the mean and median.

(b) Compute the first quartile and the third quartile.

(c) Compute the variance, standard deviation, and range.

(d) Construct a box-and-whisker plot.

(e) Are the data skewed? If so, how?

(f) Based on the results of (a) through (d), what conclusions can you reach concerning the miles per gallon of midsized sedans?

Question # 554 - A survey of 1,085 adults asked, “Do you enjoy shopping for clothing for yourself?” The results (data extracted from “Split decision on clothes shopping,” USA Today, 28 January 2011, p. 1B) indicated that 51% of the females enjoyed shopping for clothing for themselves, compared to 44% of the males. The sample sizes of males and females was not provided. Suppose that the results were as shown in the following table:

What is the probability that a respondent chosen at random?

(a) Enjoys shopping for clothing for himself or herself?

(b) Is a female and enjoys shopping for clothing for herself?

(c) Is a female or a person who enjoys shopping for clothing?

(a) no power outages?

(b) four power outages?

(c) at least three power outages?

Question # 556 - Accuracy in taking orders at a drive-through window is important for fast-food chains. Periodically, QSR Magazine publishes the results of a survey that measures accuracy, defined as the percentage of orders that are filled correctly. In a recent month, the percentage of orders filled correctly at Burger King was approximately 82.3%.

Suppose that you go to the drive-through window at Burger King and place an order. Two friends of yours independently place orders at the drive-through window at the same Burger King.

What are the probabilities that?

(a) All three of the three orders will be filled correctly?

(b) None of the three orders will be filled correctly?

(c) At least two of the three orders will be filled correctly?

(d) What are the mean and standard deviation of the binomial distribution for the number of orders filled correctly?

Question # 558 - The quality control manager of Marilyn’s Cookies is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 6.0. What is the probability that in any particular cookie being inspected there are?

(a) less than five chip parts?

(b) exactly five chip parts?

(c) five or more chip parts?

(d) either four or five chip parts?