Question 1: Central for Disease Control (CDC) monitors children\'s growth by mea

Question

Question 1: 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 65 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 O inch, and the standard deviation of the measurement error is 0.8 inches. If a 12 year-old patient who is 54.5 inches tall goes to the doctor, what is the probability that a that the pediatrician measures that the patient has stunted growth?

Explanation / Answer

Ans:

mean=59

standard deviation=3.8

a)P(x>65)

z=(65-59)/3.8=1.58

P(z>1.58)=1-P(z<=1.58)=1-0.9429=0.0571

b)P(x<54)

z=(54-59)/3.8=-1.32

P(z<-1.32)=0.0934

9.34% have stunted growth.

c)54.5-54=0.5

z=(0.5-0)/0.8=0.625

P(z.>0.625)=1-0.734=0.2660

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