Amaze Writers

Suppose the monthly charges for cell phone plans are normally distributed with mean μ=$68 and standard deviation σ=​$20. ​(a) Draw a normal curve with the parameters labeled. ​(b) Shade the region that represents the proportion of plans that charge less than ​$48. ​(c) Suppose the area under the normal curve to the left of X=​$48 is 0.1587. Provide an interpretation of this result. ​(a) Choose the correct graph below.     A.                   2868108X         A normal curve has a horizontal axis labeled “X” with three labeled coordinates, 28, 68, and 108. The curve’s peak is near the top of the graph at horizontal coordinate 68. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 28, 68, and 108.   B.                   486888X         A normal curve has a horizontal axis labeled “X” with three labeled coordinates, 48, 68, and 88. The curve’s peak is near the top of the graph at horizontal coordinate 68. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 48, 68, and 88.   C.                   6888108X         A normal curve has a horizontal axis labeled “X” with three labeled coordinates, 68, 88, and 108. The curve’s peak is near the top of the graph at horizontal coordinate 88. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 68, 88, and 108.   D.                   284868X         A normal curve has a horizontal axis labeled “X” with three labeled coordinates, 28, 48, and 68. The curve’s peak is near the top of the graph at horizontal coordinate 48. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 28, 48, and 68. ​(b) Choose the correct graph below.     A.                           6888108X 48         A normal curve has a horizontal axis labeled “X” with four labeled coordinates, 48, 68, 88, and 108. The curve’s peak is near the top of the graph at horizontal coordinate 88. Four vertical line segments run from the horizontal axis to the curve at horizontal coordinates 48, 68, 88, and 108. The area under the curve to the left of the vertical line segment at horizontal coordinate 48 is shaded.   B.                           2868108X 48         A normal curve has a horizontal axis labeled “X” with four labeled coordinates, 28, 48, 68, and 108. The curve’s peak is near the top of the graph at horizontal coordinate 68. Four vertical line segments run from the horizontal axis to the curve at horizontal coordinates 28, 48, 68, and 108. The area under the curve to the left of the vertical line segment at horizontal coordinate 48 is shaded.   C.                     486888X         A normal curve has a horizontal axis labeled “X” with three labeled coordinates, 48, 68, and 88. The curve’s peak is near the top of the graph at horizontal coordinate 68. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 48, 68, and 88. The area under the curve to the left of the vertical line segment at horizontal coordinate 48 is shaded.   D.                       284868X         A normal curve has a horizontal axis labeled “X” with three labeled coordinates, 28, 48, and 68. The curve’s peak is near the top of the graph at horizontal coordinate 48. Three vertical line segments run from the horizontal axis to the curve at horizontal coordinates 28, 48, and 68. The area under the curve to the left of the vertical line segment at horizontal coordinate 48 is shaded. ​(c) Select the correct choice below and fill in the answer box to complete your choice. ​(Type a whole​ number.)   A. The probability is 0.1587 that a randomly selected cell phone plan in this population is less than ​$nothing per month.   B. The probability is 0.1587 that a randomly selected cell phone plan in this population is more than ​$nothing per month.