Question

Assume that the random variable X is normally​ distributed, with mean mu equals 51μ=51 and standard deviation sigma equals 9σ=9. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Upper P left parenthesis Upper X less than or equals 48 right parenthesisP(X≤48)

Which of the following shaded regions corresponds to Upper P left parenthesis Upper X less than or equals 48 right parenthesisP(X≤48)​?

A.

X

48485151

A normal curve has a horizontal axis labeled "X" with two labeled coordinates, "48" and "51." The normal curve is slightly above the horizontal axis at the left edge of the graph, rises from left to right at an increasing and then decreasing rate to its peak at 51, the graph's horizontal center, and falls from left to right at an increasing and then decreasing rate to be slightly above the horizontal axis at the right edge of the graph. Two vertical line segments run from the horizontal axis to the curve, where one is at 48, to the left of the normal curve's peak, and the other is at 51. The area under the curve to the right of the left vertical line segment is shaded.

B.

X

48485151

A normal curve has a horizontal axis labeled "X" with two labeled coordinates, "48" and "51." The normal curve is slightly above the horizontal axis at the left edge of the graph, rises from left to right at an increasing and then decreasing rate to its peak at 51, the graph's horizontal center, and falls from left to right at an increasing and then decreasing rate to be slightly above the horizontal axis at the right edge of the graph. Two vertical line segments run from the horizontal axis to the curve, where one is at 48, to the left of the normal curve's peak, and the other is at 51. The area under the curve to the left of the left vertical line segment is shaded.

C.

X

48485151

A normal curve has a horizontal axis labeled "X" with two labeled coordinates, "48" and "51." The normal curve is slightly above the horizontal axis at the left edge of the graph, rises from left to right at an increasing and then decreasing rate to its peak at 51, the graph's horizontal center, and falls from left to right at an increasing and then decreasing rate to be slightly above the horizontal axis at the right edge of the graph. Two vertical line segments run from the horizontal axis to the curve, where one is at 48, to the left of the normal curve's peak, and the other is at 51. The area under the curve between the vertical line segments is shaded.

Upper P left parenthesis Upper X less than or equals 48 right parenthesisP(X≤48)equals= nothing

​(Round to four decimal places as​ needed.)

Answer 1

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