Answered: Suppose we have a binomial experiment…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(a)

Suppose n = 31 and
p = 0.28.

(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

n·p exceedsboth n·p and n·q exceed n·q does not exceedn·p and n·q do not exceedn·q exceedsn·p does not exceed

fourth blank (Enter an exact number.)

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

σ_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

n·p exceedsboth n·p and n·q exceed n·q does not exceedn·p and n·q do not exceedn·q exceedsn·p does not exceed

fourth blank (Enter an exact number.)

(c)

Suppose

n = 46 and
p = 0.35.

YesNo

second blank

cancannot

third blank

n·p exceedsboth n·p and n·q exceed n·q does not exceedn·p and n·q do not exceedn·q exceedsn·p does not exceed

fourth blank (Enter an exact number.)

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

σ_p̂ =

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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