Question

Suppose the lengths of human pregnancies are normally distributed with muequals266 days and sigmaequals16 days. Complete parts ​(a) and​ (b) below. ​(a) The figure to the right represents the normal curve with mu equals 266 days and sigmaequals16 days. The area to the left of Upper X equals 245 is 0.0947. Provide two interpretations of this area. Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Type integers or​ decimals.)

A. The proportion of human pregnancies that last less than __ days is ___

B. The proportion of human pregnancies that last more than __ days is ___

X font size decreased by 3 266font size decreased by 3 245 A normal curve has a horizontal axis labeled "X" and two horizontal coordinates, 245 and 266. The curve's peak is near the top of the graph at horizontal coordinate 266. Two vertical line segments run from the horizontal axis to the curve at 245 and 266. The area under the curve to the left of 245 is shaded.

Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Type integers or​ decimals.)

A. The probability that a randomly selected human pregnancy lasts less than___days is ___.

B. The probability that a randomly selected human pregnancy lasts more than ___ days is ___.

​(b) The figure to the right represents the normal curve with mu equals 266 days and sigmaequals16 days. The area between xequals290 and x equals 305 is 0.0594. Provide two interpretations of this area. Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Type integers or decimals. Use ascending​ order.)

A. The proportion of human pregnancies that last between ____ and ___ days is ___.

B. The proportion of human pregnancies that last less___ or more than n

Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Type integers or decimals. Use ascending​ order.)

A.The probability that a randomly selected human pregnancy lasts between

___

and

____

days is

_____

B.The probability that a randomly selected human pregnancy lasts less than

____

or more than

_____

days is

_____

Answer 1

Solution :

Given that ,

mean = = 266

standard deviation = =16

a) P(x < 245) =0.0947

A) The proportion of human pregnancies that last less than 245 days is 0.0947

A) The probability that a randomly selected human pregnancy lasts less than 245 days is 0.0947

b) P(290 < x < 305) =0.0594

A) The proportion of human pregnancies that last between 290 and 305 days is 0.0594

A) The probability that a randomly selected human pregnancy lasts between 290 and 305 days is 0.0594