Question

Need help with this assignment. Any help is appreciated. This has to be written clearly so i can see it & in good english. For the directions don't do step 3. Need this done ASAP!

Statistics: Problem Set2 Directions: 1. Solve the following problems. Hand write your solutions and explanations on your own paper. Do not write answers on this page. Show your work AND explain your reasoning using complete English sentences. Explanations must directly follow the solution for each part of the problem. 2. 3. You must write your name on the top right of the paper you turn in 4. You must write the title of this problem set on the top of your paper 5. Turn in your solutions following the directions in the assignment information on Canvas. 1. The table below shows a frequency distributions for the heights of all Major League Baseball players from 1876-2012.(Source Height inches 63 to 65 66 to 68 69 to 71 72 to 74 75 to 77 78 to 80 81 to 83 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. a. [2 pts] 10% of men are taller than which height? Round your answer to 1 b. [2 pts]Find the percentage of men that are 6'0" or taller. Round your final c. [1 pts]How does the approximate percentage for the height of men 6'0" or d. 1 pts]Based on your normal distribution calculation from part (b), decimal place. answer to 2 decimal places. taller (from the normal distribution) compare with the actual percentage of baseball players 6'0" or taller (from Problem 1)? approximately how many Major League Baseball players would you expect to be 6'0" or taller? Round your answer to the nearest whole number

Answer 1

Answer 1

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

Answer 1 a Total number of people that have played Major Laegue Baseball between 1876 and 2012 is

(73+1056+..................+11) = 16933

Answer 1 b 6'0" = (12*6+0) inches = 72 inches

Number of Major Laegue Baseball player 6'0" or taller is (7593+2903+...... +11) = 10798

Hence percentage of Major Laegue Baseball player 6'0" or taller is (10798/16933) *100% = 63.77%

Answer 2

We are given that sample mean ($\mu$) = 69.7 inches and stander deviation ($\sigma$) = 2.9 inches

Answer 2 a

Suppose 10% men are taller than height X inches which equivalent to say 90% men are smaller than height X inches

Now from stander normal table we have, 90 percentile Z-score is 1.28

Hence we need to solve X(inches) from following

X- 69.7 2.9 1.28

X= 69.7 + 1.28 * 2.9 = 73.41 inches

Answer 2 b

We know that 6'0" = (12*6+0) inches = 72 inches

We have to find Pr(X>=72) = ?

which is equivalent to find 1- Pr(X<72) =?

Now Pr(X<72)

X-69.7 2.9 72-69.7 2.9 Pr(

X-69.7 2.9 72-69.7 2.9 Pr(

Pr(Z<0.793103)
where
X-69.7 ollows N(0, 1) 2.9

= 0.786141

  hence Pr(X>=72) = 1 - 0.786141 = 0.2139

Therefore 21.39% men are  6'0" or taller

Answer 2 c

	Normal distribution	baseball players(prob 1)
Height 6'0" or more	21.39%	63.77%

Answer 2 d

Since total number Major Laegue Baseball player is 16933

Number of Major Laegue Baseball player expected to be  6'0" or taller is 16933* 21.39% = 3621