Question

An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 90 and a standard deviation of 12. Use StatCrunch to find the proportion of children have an index of at least 110.

Answer 1

Answer:

The proportion of children that have an index of at least 110 is 0.0478.

Step-by-step explanation:

The given distribution has a mean of 90 and a standard deviation of 12.

Therefore mean, $\mu$ = 90 and standard deviation, $\sigma$ = 12.

It is given to find the proportion of children having an index of at least 110.

We can take the variable to be analysed to be x = 110.

Therefore we have to find p(x < 110), which is left tailed.

Using the formula for z which is p( Z < $\frac{x - \mu}{\sigma}$) we get p(Z < $\frac{110 - 90}{12}$ = 1.67).

So we have to find p(Z ≥ 1.67) = 1 - p(Z < 1.67)

Using the Z - table we can calculate p(Z < 1.67)  = 0.9522.

Therefore p(Z ≥ 1.67) = 1 - 0.9522 = 0.0478

Therefore the proportion of children that have an index of at least 110 is 0.0478