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Do question 3

Suppose that the heights of college women follow a normal distribution with a mean 65
inches and a standard deviation 2.5 inches.
Use this information to answer the following 3 problems.
1. Gloria is 62 inches tall. Approximately what percent of college women are shorter than
Gloria?
11.51%
2. Isabel is a player in the women's basketball team. How tall is Isabel if 15% of college
women are taller than her?
67.6 inches
3. Let Y= the number of college women who are at least 65 inches tall in a random sample
of 150.
[ Select ]
Binomial (150, 0.50)
Normal (65, 2.5)
Normal (75, 6.124)
Binomial (150, 0.65)
What is the exact model of Y?
Transcribed Image Text:Suppose that the heights of college women follow a normal distribution with a mean 65 inches and a standard deviation 2.5 inches. Use this information to answer the following 3 problems. 1. Gloria is 62 inches tall. Approximately what percent of college women are shorter than Gloria? 11.51% 2. Isabel is a player in the women's basketball team. How tall is Isabel if 15% of college women are taller than her? 67.6 inches 3. Let Y= the number of college women who are at least 65 inches tall in a random sample of 150. [ Select ] Binomial (150, 0.50) Normal (65, 2.5) Normal (75, 6.124) Binomial (150, 0.65) What is the exact model of Y?
Expert Solution
Step 1

Sampling Distribution of a Normal Variable : 


Given a random variable X. Suppose that the population distribution of X is known to be normal, with mean µ and
variance σ2 , that is, X ~ N(µ, σ). Then, for any sample size n, it follows that the sampling distribution of X¯ is normal,
with mean µ and variance σ2/n , that is, 

                                X¯ ~ N μ,σn

  • σnis called the “standard error of the mean,” denoted SEM, or more simply, s.e. 
  • The corresponding Z-score transformation formula is  Z=X¯-μσ/n ~ N(0,1) . 

 

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