Central for Disease Control (CDC) monitors children’s growth by measuring their

Question

Central for Disease Control (CDC) monitors children’s growth by measuring their height each year. They found that at age of 12, a child has an average height of 59 inches. Assume that the height of a 12 year-old child is normally distributed with a standard deviation of 3.8 inches. The CDC also considers 12 year-olds who are 54 inches tall or shorter to have stunted growth. Use this information and answer Questions 1a to 1c

Question 1a:

What is the probability that a 12-year-old is taller than 62 inches?

Question 1b:

What is the proportion of the 12 year-olds that that have stunted growth?

Question 1c:

Assume that when pediatricians measure the height of patients, that there is measurement error which is normally distributed. The mean of the error is 0 inch, and the standard deviation of the measurement error is 0.5 inches. If a 12 year-old patient who is 55 inches tall goes to the doctor, what is the probability that a that the pediatrician measures that the patient has stunted growth?

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 59
standard Deviation ( sd )= 3.8
a.
P(X > 62) = (62-59)/3.8
= 3/3.8 = 0.7895
= P ( Z >0.7895) From Standard Normal Table
= 0.2149
b.
P(X > 54) = (54-59)/3.8
= -5/3.8 = -1.3158
= P ( Z >-1.3158) From Standard Normal Table
= 0.9059
c.
not sure how to proceed

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects