SOLUTION: an someone help me show step by step the correct ansers to these questions i did incorrectly on my test Thankyou. It will be greatly appreciated. Step by Step answers Thankyou

Question 76076: an someone help me show step by step the correct ansers to these questions i did incorrectly on my test Thankyou. It will be greatly appreciated. Step by Step answers Thankyou
1. The mean height of women in the U.S.(ages 20-29) is 64. inches and the standard deviation is 2.75 inches. If a women is selected at random, what is the probability that she will have a height between 61.23 and 65.99 inches?
Show standard normal graph and label z-scores.
b. If 8 women are selected at random what is the probability that they will have a mean height of between 65. and 66.56 inches? Show graph.

2. Assume each student chooses exactly 1 major.
27.70% Education, 11.11%english, 6.37%Math, 54.81%ISM.
A. If 8 students are randomly selected, what is the probability that exactly 6 of them will NOT be ISM majors?
B. If 8 students are randomly selected, what is the probability that exactly 7 of them will be ISM or English majors?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. The mean height of women in the U.S.(ages 20-29) is 64. inches and the standard deviation is 2.75 inches. If a women is selected at random, what is the probability that she will have a height between 61.23 and 65.99 inches?
Show standard normal graph and label z-scores.
-------
z(61.23)=(61.23-64)/2.75= -1.00
z(65.99)=(65.99-64)/2.75= 0.7236
P(-1,0<=z<=0.7236)=0.6067
------------------
b. If 8 women are selected at random what is the probability that they will have a mean height of between 65. and 66.56 inches? Show graph.
-----
Find the z-scores of 65 and 66.56 using a standard deviation of 2.75/sqrt(8)
For example: z(65)=(65-64)/2.75/sqrt8)=1/0.97=1.0285
z(66.56)=2.56/0.97=2.639
P(1.0285 ===============
2. Assume each student chooses exactly 1 major.
27.70% Education, 11.11%english, 6.37%Math, 54.81%ISM.
A. If 8 students are randomly selected, what is the probability that exactly 6 of them will NOT be ISM majors?
------
P(ISM)=0.81
This is a binomial problem with n=8 ; p=0.81 ; x=6
P(x=6)=8C6(0.81)^6(0.19)^2 =0.2855

B. If 8 students are randomly selected, what is the probability that exactly 7 of them will be ISM or English majors?
Add the probabilities because the events are disjoint.
P(ism)=0.81; P(eng)=0.11
P(ism or eng)=0.92
Binomial with n=8 ; p=0.92 ; x=7
P(x=7)=0.357
==========
Cheers,
Stan H.

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