Question

The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 269 days and a standard deviation of 8 days. ​(a) What is the minimum pregnancy length that can be in the top 12% of pregnancy​ lengths? ​(b) What is the maximum pregnancy length that can be in the bottom 3​% of pregnancy​ lengths?

Answer 1

Answer:

a) 279 b)254

Step-by-step explanation:

Mean = 269 days

standard deviation = 8 days

let n be the pregnancy lenght.  

using normal distribution formula

z = (n – mean)/ standard deviation

n = z * standard deviation + mean

Now, z values for the top 12% has to be found using a z table.

The top 12% means 88% of area under the curve. In this case z = 1,176

n = 1,176 * 8 + 269

n = 278.4 = 279

The bottom 3% means 97% of area under the curve. In this case z = -1,882

n = -1,882 * 8 + 269

n = 253.94 = 254