Question

Suppose the lengths of human pregnancies are normally distributed with

mean= 266days and standard deviations =16 days. Complete parts ​(a) and​ (b)below.

(a) The figure to the right represents the normal curve with

mean is  266 days and standard deviation 16days. The area to the left of X= 245 is 0.0947. Provide two interpretations of this area.

​(b) The figure to the right represents the normal curve with mean is 266 days and the standard deviation is 16days. The area between x= 235 and x= 250 is 0.1323. Provide two interpretations of this area.

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Answer 1

We have, mean= 266 days and standard deviations =16 days.

a) The area to the left of X= 245 is 0.0947. Provide two interpretations of this area.

1) It indicates P(X < 245) = 0.0947

2) It indicates 9.47% of the data values are having value less than 245

3) It indicates P(X > 245) = 1 - 0.0947 = 0.9053

b) The area between x= 235 and x= 250 is 0.1323. Provide two interpretations of this area.

1) It indicates P(235 < x < 250) = 0.1323

2) It indicates 13.23% of the data values are having values in the range (235,250)

3) It indicates, P(x < 235) + P(x > 250) = 1 - 0.1323 = 0.8677