Answered: (a) Suppose n = 26 and p = 0.23. (For…

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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(a)

Suppose n = 26 and
p = 0.23.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q = ?

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

cancannot

third blank

both n·p and n·q exceedn·q exceeds n·p and n·q do not exceedn·q does not exceedn·p exceedsn·p does not exceed

fourth blank (Enter an exact number.)
?

What are the values of ?_p̂ and ?_p̂? (For each answer, enter a number. Use 3 decimal places.)
?_p̂ = mu sub p hat =

?_p̂ = sigma sub p hat =

(b)

Suppose

n = 25 and
p = 0.15.

Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo

second blank

cancannot

third blank

both n·p and n·q exceedn·q exceeds n·p and n·q do not exceedn·q does not exceedn·p exceedsn·p does not exceed

fourth blank (Enter an exact number.)

(c)

Suppose

n = 48 and
p = 0.35.

YesNo

second blank

cancannot

third blank

both n·p and n·q exceedn·q exceeds n·p and n·q do not exceedn·q does not exceedn·p exceedsn·p does not exceed

fourth blank (Enter an exact number.)

?

What are the values of ?_p̂ and ?_p̂? (For each answer, enter a number. Use 3 decimal places.)
?_p̂ = mu sub p hat =

?_p̂ = sigma sub p hat =

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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