Problem 4: Suppose 85% of a certain product actually satisfy the requirement, an

Question

Problem 4: Suppose 85% of a certain product actually satisfy the requirement, and we have 25 of such products. Let X be the number of products satisfy the requirement.

a) What is the name of this distribution? Circle the correct answer. (1 point) A) Discrete Distribution. B) Sampling Distribution about the Mean C) Normal Distribution D) Binomial Distribution

b) Find the probability that exactly 15 products satisfy the requirement (4 points)

c) Find the population mean and standard deviation. (2 points)

d) Now assume that the distribution is actually normal, and a sample of 36 of such products has selected. Find the probability that the mean number of products satisfy the requirement is at least 16. (3 points)

Explanation / Answer

a.
D) Binomial Distribution
b.
P( X = 15 ) = ( 25 15 ) * ( 0.85^15) * ( 1 - 0.85 )^10
= 0.0016
c.
Mean ( np ) =25 * 0.85 = 21.25
Standard Deviation ( npq )= 25*0.85*0.15 = 1.7854
Normal Distribution = Z= X- u / sd                   
d.
Normal Approximation to Binomial Distribution
Mean ( np ) =36 * 0.85 = 30.6
Standard Deviation ( npq )= 36*0.85*0.15 = 2.1424
Normal Distribution = Z= X- u / sd                   
P(X > 16) = (16-30.6)/2.1424
= -14.6/2.1424 = -6.8148
= P ( Z >-6.815) From Standard Normal Table
= 1                  

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.