Assume that the random variable X is normally distributed, with mean

mu

equals50

and standard deviation

sigma

equals10

.

Compute the probability

P(38

less thanXless than or equals55

).

Be sure to draw a normal curve with the area corresponding to the probability shaded.

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Part 1

Draw a normal curve with the area corresponding to the probability shaded. Choose the correct graph below.

A.

3855x

A normal curve has a horizontal axis labeled "x" with two horizontal coordinates, 38 and 55. There is a dashed vertical line segment running from the horizontal axis to the curve at its peak at the horizontal center of the graph. Two solid vertical line segments run from the horizontal axis to the curve that are on either side of the curve's peak at horizontal coordinates 38 and 55. The solid vertical line segment at horizontal coordinate 55 is closer to the peak than the other solid vertical line segment. The area under the curve and to the left of the vertical line segment at 55 is shaded.

B.

3855x

A normal curve has a horizontal axis labeled "x" with two horizontal coordinates, 38 and 55. There is a dashed vertical line segment running from the horizontal axis to the curve at its peak at the horizontal center of the graph. Two solid vertical line segments run from the horizontal axis to the curve that are on either side of the curve's peak at horizontal coordinates 38 and 55. The solid vertical line segment at horizontal coordinate 55 is closer to the peak than the other solid vertical line segment. The areas under the curve to the left of the solid vertical line segment at 38 and to the right of the vertical line segment at 55 are shaded.

C.

3855x

A normal curve has a horizontal axis labeled "x" with two horizontal coordinates, 38 and 55. There is a dashed vertical line segment running from the horizontal axis to the curve at its peak at the horizontal center of the graph. Two solid vertical line segments run from the horizontal axis to the curve that are on either side of the curve's peak at horizontal coordinates 38 and 55. The solid vertical line segment at horizontal coordinate 55 is closer to the peak than the other solid vertical line segment. The area under the curve and between the two solid vertical line segments is shaded.

Part 2

P(38

less thanXless than or equals55)equals59.93

(Round to four decimal places as needed.)