3 math project

You will be performing an analysis on heights in the US population, broken out by gender. You will need to know that US heights for males and females both follow an approximately normal distribution. The average height for women is 63.7 inches and a standard deviation of 2.7 inches. The average height for men is 69.1 inches and a standard deviation of 2.9 inches. You will use these numbers in your calculations.

Steps (all statistical analysis to be done in Excel and/or StatCrunch):

1. Collect the heights from 5 females and 5 males that you know. Make sure that you put all heights into inches. Include yourself in the analysis (as one of the 10).

2. Normal Distribution application:

a. Calculate z-scores for each of the selected people and provide interpretations for at least 2 of your z-scores (after looking up probabilities on the table). You also need to include interpretations that indicate how “rare” your observations are in the body of your paper. (Ex: Individual A from my sample with a height of ______ had a corresponding z-score of _____. This means that _______% of people are taller/shorter than him/her)

b. Include one graphic that shows the normal curve along with labels for the middle 68%, 95% and 99.7%. Also show where your own height is on the curve along with an interpretation of how relatively “tall” or “short” you are in comparison with the rest of your gender.

c. Calculate the mean of your male heights and female heights and compare this with the population mean (is it above/below – why is it not exact).

d. Calculate z-scores for the average heights of WNBA and NBA players (typically much taller than the average person) and also male jockeys (typically quite a bit shorter than the average person). Provide interpretations for each.

3. Binomial Experiment application:

a. In order to be considered for a tier 1 point guard in women’s basketball, you need to be 5’8”. Let’s consider a “success” as finding a woman who is 5’8” or taller. The probability of success is approximately 5%. If we consider a sample of 1000 women, calculate the mean and the standard deviation of the binomial random variable.

b. Calculate the range of “normal” observations (not unusual) for the number of women that we would expect to be 5’8” or taller in a sample of 1000 women and use it in a sentence.

c. Use a binomial calculator to calculate the probability of selecting*:

i. Less than 40 women who are 5’8” or taller

ii. Exactly 60 women who are 5’8” or taller

iii. Between 50 and 80, inclusive, women who are 5’8” or taller

iv. More than 70 women who are 5’8” or taller

v. At least 60 women who are 5’8” or taller

*Don’t just give answers here, use complete sentences. Graphs would be a nice addition here (StatCrunch screen grabs or Excel graphs).

d. Can we use the normal distribution as an approximation for the binomial in this case? Why or why not? If yes, what is the probability that we would choose less than 40 women who are 5’8” or taller using this approximation? How does this value compare with the value calculated in part c(i) above?

4. Put everything together into an organized paper and submit on IvyLearn.