Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 26 and p = 0.38. (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 Yes No second blank can cannot third blank n·q does not exceed n·p and n·q do not exceed n·p exceeds n·q exceeds n·p does not exceed both n·p and n·q exceed fourth blank (Enter an exact number.) _________________. What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.) μp̂ = mu sub p hat = σp̂ = 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 Yes No second blank can cannot third blank n·q does not exceed n·p and n·q do not exceed n·p exceeds n·q exceeds n·p does not exceed both n·p and n·q exceed fourth blank (Enter an exact number.) ________________. (c) Suppose n = 41 and p = 0.22. (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 Yes No second blank can cannot third blank n·q does not exceed n·p and n·q do not exceed n·p exceeds n·q exceeds n·p does not exceed both n·p and n·q exceed fourth blank (Enter an exact number.) _____________________ What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.) μp̂ = mu sub p hat = σp̂ = sigma sub p hat =

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 26 and p = 0.38. (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 Yes No second blank can cannot third blank n·q does not exceed n·p and n·q do not exceed n·p exceeds n·q exceeds n·p does not exceed both n·p and n·q exceed fourth blank (Enter an exact number.) _____________. What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.) μp̂ = mu sub p hat = σp̂ = 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 Yes No second blank can cannot third blank n·q does not exceed n·p and n·q do not exceed n·p exceeds n·q exceeds n·p does not exceed both n·p and n·q exceed fourth blank (Enter an exact number.) ____________. (c) Suppose n = 41 and p = 0.22. (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 Yes No second blank can cannot third blank n·q does not exceed n·p and n·q do not exceed n·p exceeds n·q exceeds n·p does not exceed both n·p and n·q exceed fourth blank (Enter an exact number.) ___________________ What are the values of μp̂ and σp̂? (For each answer, enter a number. Use 3 decimal places.) μp̂ = mu sub p hat = σp̂ = sigma sub p hat =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 5E

See similar textbooks

(a) Suppose n = 26 and p = 0.38. (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

Yes

second blank

can

cannot

third blank

n·q does not exceed

n·p and n·q do not exceed

n·p exceeds

n·q exceeds

n·p does not exceed

both n·p and n·q 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

Yes

second blank

can

cannot

third blank

n·q does not exceed

n·p and n·q do not exceed

n·p exceeds

n·q exceeds

n·p does not exceed

both n·p and n·q exceed

fourth blank (Enter an exact number.)

________________.

(c) Suppose n = 41 and p = 0.22. (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

Yes

second blank

can

cannot

third blank

n·q does not exceed

n·p and n·q do not exceed

n·p exceeds

n·q exceeds

n·p does not exceed

both n·p and n·q 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 =

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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