Let's say that an athletic clothes and accessories company is creating a next-generation, high-accuracy accelerometer for athletes to measure their movements during specific activities. The company will be tuning their devices to accurately measure exertion during swimming, cycling, walking, jogging, running, and playing games such as golf and tennis. Depending on the activity and which part of the body the user is interested in, the company anticipates that the user may wish to affix the device to either their ankle, wrist, or upper arm.

The company is trying to determine how many straps they need to include with the product and if they need to create separate men's and women's versions.

Please download the body.csv dataset. Researchers recorded body dimension measurements (cm), age (years), weight (kg), height (cm), and gender (1 = male, 0 = female) of 507 individuals (247 men, 260 women). These individuals were primarily in their twenties and thirties, with a scattering of older men and women, and they all habitually exercise several hours per day. The measurements were taken at San Jose State University in San Jose, California, U.S. Naval Postgraduate School in Monterey, California, as well as dozens of health and fitness clubs in California.

Use the variables WristMinGirth, AnkleMinGirth, and BicepGirth to answer the following questions. Let's say that only one strap that adjusts between 15 and 21 centimeters (inclusive) was included. (Round your answers to four decimal places.)

(a) Use the data to estimate the probability that a person would be able to fit the strap around his or her wrist and ankle and upper arm. -------------------

(b) Use the data to estimate the probability that a person would be able to fit the strap around his or her wrist or ankle or upper arm.---------------------

(c) Use the data to estimate the probability that a person would be able to fit the strap around his or her wrist and either his or her ankle or upper arm. -------------------------

(d) Given the company's goals, does one strap seem like a good solution to you? If in the end they only include one strap, how might they market the product and label the package?-------------------------------

Let's say that one strap that adjusts between 15 and 19 centimeters (inclusive) and another strap that adjusts between 22 and 32 centimeters (inclusive) were included. (Round your answers to four decimal places.)

(a) Use the data to estimate the probability that a person would be able to fit the straps around his or her wrist and ankle and upper arm. -------------------

(b) Use the data to estimate the probability that a person would be able to fit the straps around their wrist and either their ankle or their upper arm. ----------------

(c) Use the data to estimate the probability that a person would be able to fit the straps around their wrist or their ankle or their upper arm.--------------------

d) If they only include two straps with their product, what are the risks to their goals? How might they market the product and label the package?---------------

Consider men's and women's versions of the product. (Round your answers to four decimal places.)

(a) Let's say that one strap that adjusts between 14 and 17 centimeters (inclusive) and another that adjusts between 20 and 28 centimeters (inclusive) were included. Use the data to estimate the probability that a woman would be able to fit the straps around her wrist and either her ankle or her upper arm. ----------------------

b) Let's say that one strap that adjusts between 15 and 19 centimeters (inclusive) and another that adjusts between 22 and 36 centimeters (inclusive) were included. Estimate the probability that a man would be able to fit the straps around his wrist and either his ankle or his upper arm.---------------------

After careful consideration, answer the following questions.

(a) If a certain strap configuration works for 95% of the sample, could anything go wrong when the product is distributed to a larger population?

(b)Does the shape of the distribution of wrists or ankles or biceps in the larger population matter when trying to determine whether these probabilities are likely to hold in the larger population?

(c)Taking into consideration the company's goals, the calculations you've already made (plus any additional calculations you may wish to make), and your knowledge about the source of the data, what would you advise the company to do?