Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 27 and p = 0.28. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = nq = ---Select--- Yes No , p̂ ---Select--- cannot can be approximated by a normal random variable because ---Select--- np does not exceed both np and nq exceed nq does not exceed np and nq do not exceed np exceeds nq exceeds . What are the values of μp̂ and σp̂? (Use 3 decimal places.) μp̂ = σp̂ = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? ---Select--- Yes No , p̂ ---Select--- cannot can be approximated by a normal random variable because ---Select--- both np and nq exceed nq does not exceed np exceeds nq exceeds np does not exceed np and nq do not exceed . (c) Suppose n = 41 and p = 0.32. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = nq = ---Select--- Yes No , p̂ ---Select--- cannot can be approximated by a normal random variable because ---Select--- np exceeds nq exceeds np and nq do not exceed nq does not exceed np does not exceed both np and nq exceed . What are the values of μp̂ and σp̂? (Use 3 decimal places.) μp̂ = σp̂ =

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a) Suppose n = 27 and p = 0.28. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np =

nq =

---Select--- Yes No , p̂ ---Select--- cannot can be approximated by a normal random variable because ---Select--- np does not exceed both np and nq exceed nq does not exceed np and nq do not exceed np exceeds nq exceeds .

What are the values of μ_p̂ and σ_p̂? (Use 3 decimal places.)

μ_p̂ =

σ_p̂ =

(b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not?
---Select--- Yes No , p̂ ---Select--- cannot can be approximated by a normal random variable because ---Select--- both np and nq exceed nq does not exceed np exceeds nq exceeds np does not exceed np and nq do not exceed .

(c) Suppose n = 41 and p = 0.32. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np =

nq =

---Select--- Yes No , p̂ ---Select--- cannot can be approximated by a normal random variable because ---Select--- np exceeds nq exceeds np and nq do not exceed nq does not exceed np does not exceed both np and nq exceed .

What are the values of μ_p̂ and σ_p̂? (Use 3 decimal places.)

μ_p̂ =

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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