1. The serum cholesterol (SC) levels of 12-to-14-year-olds follow a normal distr

Question

1. The serum cholesterol (SC) levels of 12-to-14-year-olds follow a normal distribution with mean 155 mg/dl and standard deviation 27 mg/dl.

Using R and Z-table.

a. Find the 80th percentile (“The SC level that is higher than 80% of all 12-to-14-year-olds”) (In terms of the problem, meaning in mg/dl)

Using R and Z-table

b.Find the 20th percentile (In terms of the problem)

E.Using Z-table

2. Consider serum cholesterol levels from a random sample of 30 children ages 12-14.

You must clearly write in each case:

i) The desired probability

ii) The z-score(s)

iii) Work (math!)

iv) Final answer

10. What is the sampling distribution of the mean? Why?

11. What is the probability that the sample mean will be between 157 and 161?

12. What is the probability that the sample mean will be “high” by AHA standards?

13. What is the probability that the sample mean will be “normal” by AHA standards?

14. Assume the sample of 30 children give a mean of 161 mg/dl and a standard deviation of

24 mg/dl. How would these values affect your previous results (questions 10-13)?

15. Assume new information is provided and the serum cholesterol (SC) levels of 12-to-14-year-olds follow a Left-Skew distribution with mean155 mg/dl and standard deviation 27 mg/ dl. How this information affect your previous results (questions 10-13) ?

16. What is the probability that 15 or less children of our sample of size 30 would have a SC level of 161 mg/dl or less?

i)Use Rfor the exact probability.

ii) Can we approximate this probability using a normal distribution? Why?

iii) If we can approximate this probability using a normal distribution, please show yourwork (state desired probability, z-score(s), work, final answer) using Z-table.

iv) If we can approximate this probability using a normal distribution please check your work using R.

Explanation / Answer

(1)

Data given:

Mean, m = 155

Standard deviation, S = 27

(a)

For 80th percentile, the corresponding z-score is 0.841

So,

(X-m)/S = 0.841

Putting values:

(X-155)/27 = 0.841

So,

X = 177.71

(b)

For 20th percentile, the corresponding z-score is -0.841

So,

(X-m)/S = -0.841

Putting values:

(X-155)/27 = -0.841

So,

X = 132.29

Hope this helps !

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.