Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults in a region found that 34% name professional football as their favorite sport. You randomly select 12 adults in the region and ask them to name their favorite sport. Complete parts (a) through (d) below (c) Find the probability that the number who name professional football as their favorite sport is fewer than 6. The probability is 0.8087 0.8087. (Round to four decimal places as needed.) Part 7 Sketch the graph of the normal distribution with the indicated probability shaded. A. -210x μ=4.08 A normal curve is over a horizontal axis and is centered on 4.08. Vertical line segments extend from the horizontal axis to the curve at 4.08 and 5.5. The area under the curve to the left of 5.5 is shaded. B. -210x μ=4.08 A normal curve is over a horizontal axis and is centered on 4.08. Vertical line segments extend from the horizontal axis to the curve at 4.08, 5.5, and 6.5. The area under the curve between 5.5 and 6.5 is shaded. C. -210x μ=4.08 A normal curve is over a horizontal axis and is centered on 4.08. Vertical line segments extend from the horizontal axis to the curve at 4.08 and 6.5. The area under the curve to the left of 6.5 is shaded. D. The normal distribution cannot be used to approximate the binomial distribution

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Part 7

Sketch the graph of the normal distribution with the indicated probability shaded.

-210x

μ=4.08

A normal curve is over a horizontal axis and is centered on 4.08. Vertical line segments extend from the horizontal axis to the curve at 4.08 and 5.5. The area under the curve to the left of 5.5 is shaded.

-210x

μ=4.08

A normal curve is over a horizontal axis and is centered on 4.08. Vertical line segments extend from the horizontal axis to the curve at 4.08, 5.5, and 6.5. The area under the curve between 5.5 and 6.5 is shaded.

-210x

μ=4.08

A normal curve is over a horizontal axis and is centered on 4.08. Vertical line segments extend from the horizontal axis to the curve at 4.08 and 6.5. The area under the curve to the left of 6.5 is shaded.

The normal distribution cannot be used to approximate the binomial distribution.

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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