Question

Assume the random variable X is normally distributed with mean mu equals 50?=50 and standard deviation sigma equals 7?=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35) LOADING... Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35)?? A. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve between the vertical line segments is shaded. B. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the right of the left vertical line segment is shaded. C. 35355050 A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the left of the left vertical line segment is shaded. Upper P left parenthesis Upper X greater than 35 right parenthesisP(X>35)equals=nothing ?(Round to four decimal places as? needed.)

Answer 1

B. A normal curve has a horizontal axis with two labeled coordinates, 35 and 50. The curve's peak is near the top of the graph at horizontal coordinate 50. Two vertical line segments run from the horizontal axis to the curve at horizontal coordinates 35 and 50. The area under the curve to the right of the left vertical line segment is shaded; P(X > 35) = 0.9838

Explanation:

The middle line in a normal distribution represents the mean. The mean of this distribution is 50; this means the peak of the curve will have a vertical line down to the horizontal axis at 50.

The value we are concerned with is anything more than 35. This means there will be a vertical line from the horizontal axis to the curve at 35. Since we want the probability X is greater than 35, the area to the right of this value under the curve will be shaded.

To find the probability, we use a z score. The formula for z scores is

`x=(X-\mu)/(\sigma)`

Using our values for X, the mean and the standard deviation, we have

`z=(35-50)/(7)=(-15)/(7)=-2.14`

Using a z table, we see that the area under the curve to the right of this value is 0.0162. This means the area to the left, the desired area, is

1-0.0162 = 0.9838.