Question

Assume the random variable X is normally distributed with mean mu equals 50 and standard deviation sigma equals 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. Upper P left parenthesis 35 less than Upper X less than 58 right parenthesis Which of the following normal curves corresponds to Upper P left parenthesis 35 less than Upper X less than 58 right parenthesis​? A. 355058 A normal curve has a horizontal axis with three labeled coordinates, 35, 50, and 58. The curve's peak is near the top of the graph at horizontal coordinate 50. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35, 50, and 58. The areas under the curve to the left of the vertical line segment at horizontal coordinate 35 and to the right of the vertical line segment at horizontal coordinate 58 are shaded. B. 355058 A normal curve has a horizontal axis with three labeled coordinates, 35, 50, and 58. The curve's peak is near the top of the graph at horizontal coordinate 50. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35, 50, and 58. The area under the curve between the vertical line segments at horizontal coordinates 35 and 58 is shaded. This is the correct answer.C. 35,50,58 A normal curve has a horizontal axis with three labeled coordinates, 35, 50, and 58. The curve's peak is near the top of the graph at horizontal coordinate 50. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35, 50, and 58. The area under the curve to the left of the vertical line segment at horizontal coordinate 58 is shaded. Your answer is not correct. Upper P left parenthesis 35 less than Upper X less than 58 right parenthesisequals nothing ​(Round to four decimal places as​ needed.)

Answer 1

P(35<X<58)=?

We need to find Z values at 35 and 58

Z= (Xbar-mu)/sd

=(35-50)/7

=-2.142857

and

Z= (Xbar-mu)/sd

=(58-50)/7

=1.142857

P(-2.1428 <X<1.1428) (From Z table we can find Area under the normal distribution curve as)

=0.8573887

Hence 0.8573887 is the probability of P(35<X<58)

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