Answered: Assume the random variable X is…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Assume the random variable X is normally distributed with mean

μ=50

and standard deviation

σ=7.

Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

P(34<X<63)

Click the icon to view a table of areas under the normal curve.

Which of the following normal curves corresponds to

P(34<X<63)?

A normal curve has a horizontal axis with three labeled coordinates, 34, 50, and 63. 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 34, 50, and 63. The area under the curve between the vertical line segments at horizontal coordinates 34 and 63 is shaded.

A normal curve has a horizontal axis with three labeled coordinates, 34, 50, and 63. 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 34, 50, and 63. The areas under the curve to the left of the vertical line segment at horizontal coordinate 34 and to the right of the vertical line segment at horizontal coordinate 63 are shaded.

A normal curve has a horizontal axis with three labeled coordinates, 34, 50, and 63. 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 34, 50, and 63. The area under the curve to the left of the vertical line segment at horizontal coordinate 63 is shaded.

P(34<X<63)=nothing

(Round to four decimal places as needed.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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