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daser333 [38]
3 years ago
15

A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random

sample of 200 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than 0.02, the entire shipment is returned to the vendor. What is the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.05
Mathematics
1 answer:
g100num [7]3 years ago
6 0

Answer:

97.4% probability

Step-by-step explanation:

Since there is only two possible outcome of inspecting the catridge : either defective or not, we can solve the problem using the binomial probability distribution (approximated to normal).

To approximate the binomial probability to normal, we find the expected value and the standard deviation of the probability of exactly x sucesses on n repeated trials with p probability

Expected values E(X) = np

Standard deviation √V(X) = √np(1-p)

using the z-score formula (X - μ)/σ, we can solve normally distributed problem.

Where μ is the mean and σ is the standard deviation. The Z-score is is the measure of how much a sample is from the mean. The p-value associated with this z-score which is the probability that the value of the measure is smaller than X can be checked on the z-score table.

FOR THIS QUESTION,

a random sample of 200 cartridges is selected

n = 200

Therefore If there are more than 0.02 × 200 = 4 defective, the sample will be returned.

To determine the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.05

μ = E(X)

= 0.05 × 200 = 10

σ = √V(X) = √np(1-p)

= √200 × 0.05 × 0.95

= 3.08

This probability is 1 subtracted by the pvalue of Z when X =4

Z = (X - μ)/σ

Z= (4 - 10)/3.08

Z = -1.95

Z = -1.95 has a P-value of 0.026 (on the z-score table)

This means that there is a 1 - 0.026 = 0.974

= 97.4% probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.05.

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Step-by-step explanation:

I suppose that the options are:

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Depending on the number of terms of the polynomial, it takes different names.

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So if we want to find a monomial, then we need to look at the options with only one term.

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8 0
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Suppose you always eat a particular brand of cookies out of the standard sized package it comes in from the store. You notice th
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Step-by-step explanation:

The given parameter for the number of cookies are;

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The number of cookies in a package = 91 cookies

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