Show your work AND explain your reasoning using complete English sentences. Expl

Question

Show your work AND explain your reasoning using complete English sentences. Explanations must directly follow the solution for each part of the problem 1. The table below shows a frequency distributions for the heights of all Major League Baseball players from 1876-2012 Height inches 63 to 65 66 to 68 69 to 71 72 to 74 75 to 77 78 to 80 81 to 8:3 Frequency 73 1056 5006 7593 2903 291 a. [2 pts]What is the total number of people that have played Major League Baseball between 1876 and 2012? b. [2 pts]What is the percentage of Major League Baseball players 6'0" or taller? Round your answer to 2 decimal places. 2. The mean height of men is 69.7 inches. Assume that the heights of men are normally distributed, with a standard deviation of 2.9 in. [2 pts] 10% of men are taller than which height? Round your answer to 1 [2 pts] Find the percentage of men that are 6'0" or taller. Round your final [1 pts] How does the approximate percentage for the height of men 6'0" or a. decimal place b. answer to 2 decimal places c. taller (from the normal distribution) compare with the actual percentage of baseball players 6'0" or taller (from Problem 1)? d. [1 pts]Based on your normal distribution calculation from part (b), approximately how many Major League Baseball players would you expect to be 6'0" or taller? Round your answer to the nearest whole number.

Explanation / Answer

Part a

We are given a following data:

Height (inches)

Frequency

63 to 65

73

66 to 68

1056

69 to 71

5006

72 to 74

7593

75 to 77

2903

78 to 80

291

81 to 83

11

Total

16933

What is the total number of people that have played Major League Baseball between 1876 and 2012?

Answer:

From the above table, the total number of people that have played Major League Baseball between 1876 and 2012 is given as 16933.

What is the percentage of Major League Baseball players 6’0’’or taller?

Answer:

We know 1 Feet = 12 inch

So, 6’0’’ = 12*6 = 72 inch

Number of players having height of 72 inch or more = 7593 + 2903 + 291 + 11 = 10798

Proportion of Major League Baseball players 6’0’’or taller = 10798/16933 = 0.63769

Proportion of Major League Baseball players 6’0’’or taller = 0.6377

Percentage of Major League Baseball players 6’0’’or taller = 63.77%

Part b

We are given mean = 69.7

Population standard deviation = SD = 2.9

Question 1

We have to find the cut-off point for height for upper 10% heights.

X = Mean + Z*SD

Z for upper 10% = 1.28155

(By using normal Z table or excel)

X = 69.7 + 1.28155*2.9

X = 73.4165

Required height = 73.4 inch

Question 2

We have to find P(X>6’0’’) = P(X>72 inch)

P(X>72) = 1 – P(X<72)

Z = (X – mean) / SD

Z = (72 – 69.7) / 2.9 = 0.793103

P(X<72) = P(Z<0.793103) = 0.786141

(By using normal Z table or excel)

P(X>72) = 1 – P(X<72) = 1 - 0.786141 = 0.213859

Required proportion = 0.2139

Required percentage = 21.39%

Question 3

Actual percentage of baseball players 6’0’’ or taller is given as 63.77%.

Approximate percentage of baseball players 6’0’’ or taller from normal distribution is given as 21.39%.

So, approximate percentage of baseball players 6’0’’ or taller from normal distribution is very less than Actual percentage of baseball players 6’0’’ or taller.

Question 4

From part b, we are given the proportion of baseball players 6’0’’ or taller = 0.2139

Total number of players = 16933

Expected players having height 6’0’’ or taller = 16933*0.2139 = 3621.969

Required answer = 3622

Height (inches)

Frequency

63 to 65

73

66 to 68

1056

69 to 71

5006

72 to 74

7593

75 to 77

2903

78 to 80

291

81 to 83

11

Total

16933

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