The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. What proportion of children have MDI of at least 80?

Question

Reynaldo Zamora

Mathematics

5 November, 17:32

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. What proportion of children have MDI of at least 80?

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Geovanni Waters · Answer 1

0.8944

Step-by-step explanation:

The proportion of children have MDI of at least 80=P (X≥80)

P (X≥80) = P ((X-mean) / sd≥ (80-100) / 16)

We are given that mean=100 and standard deviation=sd=16. So,

P (X≥80) = P (z≥-20/16)

P (X≥80) = P (z≥-1.25)

P (X≥80) = P (-1.25
P (X≥80) = 0.3944+0.5

P (X≥80) = 0.8944

Thus, the proportion of children have MDI of at least 80 is 0.8944 or 89.44%