Question

Calcium levels in people are normally distributed with a mean of 9.7mg/dL and a standard deviation of 0.3mg/dL. Individuals with calcium levels in the bottom 15

% of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.Calcium levels in people are normally distributed with a mean of

9.7mg/dL and a standard deviation of 0.3mg/dL. Individuals with calcium levels in the bottom 15% of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

Answer 1

Solution:

Given: Calcium levels in people are normally distributed with a mean of 9.7mg/dL and a standard deviation of 0.3mg/dL.

That is X =  Calcium levels in people follows Normal distribution with and

Individuals with calcium levels in the bottom 15% of the population are considered to have low calcium levels.

We have to find x value such that:

P( X < x ) = 15%

P( X < x ) = 0.1500

Thus find z value such that:

P( Z< z ) = 0.1500

Look in z table for Area = 0.1500 or its closest area and find corresponding z value.

Area 0.1492 is closest to 0.1500 and it correspond to -1.0 and 0.04

thus z = -1.04

Now use following formula to find x value:

mg/dL

Thus the calcium level that is the borderline between low calcium levels and those not considered low is 9.4 mg/dL