The Mental Development Index (MDI) of the Bayley Scales of Infant Development is

Question

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in observing infants over time. It is approximately normal with a mean of 100 and a standard deviation of 16.

a. What proportion or percentage of children has an MDI of at least 120?

b. What proportion or percentage of children has an MDI of at least 80?

c. Find the MDI score that is the 99th percentile.

d. Find the MDI score such that only 1% of the population has an MDI score below it.

e. Recall what percentages that Q1 and Q3 represent. Find the scores for the lower quartile and upper quartile of the MDI and state them in a descriptive sentence describing what the scores represent.

f. Find the interquartile range (IQR) of the MDI scores.

g. Find the upper and lower limits and state the intervals of MDI scores that would be considered potential outliers.

Explanation / Answer

Mean is 100 and SD is 16

A. P(x>120)= P(z>(120-100)/16)= P(z>1.25) or 1-P(z<1.25) . From the normal distribution table it is 1-0.8944 or .1056

B. P(x>80) = P(z> (80-100)/16) = P(z> -1.25) which is also P(z<1.25) or 0.8944

C. Since we want the score at 0.99 area under normal curve we get z value of 2.33 from the normal distribution tbale for this. Thus it is x= 2.33*16+100= 137.28

D. This is the complement of the previous problem and thus it is given by x= -2.33*16+100 = 62.72

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