Question

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

mu equals 53μ=53

and standard deviation

sigma equals 11σ=11.

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 40 right parenthesisP(X≤40)

Which of the following shaded regions corresponds to

Upper P left parenthesis Upper X less than or equals 40 right parenthesisP(X≤40)​?

A.X

4040

5353

A normal curve has a horizontal axis labeled "X" with two labeled coordinates, "40" and "53." 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 53, 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 40, to the left of the normal curve's peak, and the other is at 53. The area under the curve to the left of the left vertical line segment is shaded.

B.X

4040

5353

A normal curve has a horizontal axis labeled "X" with two labeled coordinates, "40" and "53." 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 53, 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 40, to the left of the normal curve's peak, and the other is at 53. The area under the curve to the right of the left vertical line segment is shaded.

C.X

4040

5353

A normal curve has a horizontal axis labeled "X" with two labeled coordinates, "40" and "53." 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 53, 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 40, to the left of the normal curve's peak, and the other is at 53. The area under the curve between the vertical line segments is shaded.

Upper P left parenthesis Upper X less than or equals 40 right parenthesisP(X≤40)equals=nothing

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

Answer 1

53 P(X40) PX5 A0 53 14 メ- 53 ubue 2 is a stl normal vaute = 2 -11) 1- 301 ニ|- ○8810 ニ0.1190 40 ら3 To 1A Fin& 40 53 Ray area PL40XS く53 40 53 くX-53 く 53-53 1 1 11 - P18 ヌく0 人s a SNV O 50-1+ o 8810 = 0.3810 Aws 1 -