Question

The lengths of human pregnancies are normally distributed with

muμequals=266

days and

sigmaσequals=16

days. Complete parts ​(a) and ​(b)

below.

​(a) The following figure represents the normal curve with mu equals 266μ=266 days and sigmaσequals=1616 days. The area to the leftleft of Upper X equals 235X=235 is 0.02630.0263. Provide an interpretation of this area. Choose the correct answer below. A.The proportion of human pregnancies that last lessless than 235235 days is 0.97370.9737. B.The proportion of human pregnancies that last moremore than 235235 days is 0.02630.0263. C.The proportion of human pregnancies that last lessless than 266266 days is 0.47370.4737. D.The proportion of human pregnancies that last lessless than 235235 days is 0.02630.0263.

X font size decreased by 3 266266 font size decreased by 3 235235 A normal curve has a horizontal axis labeled "X" and two horizontal coordinates, 235 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 235 and 266. The area under the curve to the left of 235 is shaded.

Provide a second interpretation of the area. Choose the correct answer below.

A.The probability that a randomly selected human pregnancy lasts

lessless

than

235235

days is

0.97370.9737.

B.The probability that a randomly selected human pregnancy lasts

lessless

than

235235

days is

0.47370.4737.

C.The probability that a randomly selected human pregnancy lasts

moremore

than

235235

days is

0.02630.0263.

D.The probability that a randomly selected human pregnancy lasts

lessless

than

235235

days is

0.02630.0263.

​(b) The following figure represents the normal curve with

mu equals 266μ=266

days and

sigmaσequals=1616

days. The area between

xequals=280280

and

x equals 295x=295

is

0.15580.1558.

Provide an interpretation of this area. Choose the correct answer below.

The proportion of human pregnancies that last for 295295 days is 0.96500.9650. B.The proportion of human pregnancies that last more than 295295 days is 0.84420.8442. C.The proportion of human pregnancies that last between 280280 and 295295 days is 0.84420.8442. D.The proportion of human pregnancies that last between 280280 and 295295 days is 0.15580.1558.

X font size decreased by 3 266266 font size decreased by 3 280280 font size decreased by 3 295295 A normal curve has a horizontal axis labeled "X" and three horizontal coordinates, 266, 280, and 295. The curve's peak is near the top of the graph at horizontal coordinate 266. Three vertical line segments run from the horizontal axis to the curve at 266, 280, and 295. The area under the curve between the vertical line segments at 280 and 295 is shaded.

Provide a second interpretation of the area. Choose the correct answer below.

A.The probability that a randomly selected human pregnancy lasts more than

295295

days is

0.84420.8442.

B.The probability that a randomly selected human pregnancy lasts for

295295

days is

0.96500.9650.

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

280280

and

295295

days is

0.84420.8442.

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

280280

and

295295

days is

0.15580.1558

Answer 1

(a)

The correct interpretation of "area to the left of X = 235 is 0.0263"

is,

D.The proportion of human pregnancies that last less than 235 days is 0.0263

The second interpretation of the area is,

D.The probability that a randomly selected human pregnancy lasts less than 235 days is 0.0263

(b)

The correct interpretation of "area between X = 280 and X = 295 is 0.1558"

is,

D.The proportion of human pregnancies that last between 280 and 295 days is 0.1558

The second interpretation of the area is,

D.The probability that a randomly selected human pregnancy lasts between 280 and 295 days is 0.1558