MATHEMATICS COLLEGE

You are trying to determine if you should accept a shipment of eggs for a local grocery store. About 4% of all cartons which are shipped have had an egg crack while traveling. You are instructed to accept the shipment if no more than 10 cartons out of the 300 you inspect have cracked eggs. What is the probability that you accept the shipment? (In other words, what is the probability that, at the most, you had 16 cartons with cracked eggs?)a. 1012.
b. 3669.
c. 5319.
d. 4681.
e. 5832.
f. 6331.

Answers

Answer 1

Answer:

Answer:

0.8809

Step-by-step explanation:

Given that:

The population proportion p = 4% = 4/100 = 0.04

Sample mean x = 16

The sample size n = 300

The sample proportion $\hat p =(x)/(n)$

= 16/300

= 0.0533

∴

$P(\hat p \leq 0.0533) = P\bigg ( \frac{\hat p - p}{\sqrt{(P(1-P))/(n)}}\leq\frac{0.0533 - 0.04}{\sqrt{(0.04(1-0.04))/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{(0.04(0.96))/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{(0.0384)/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{1.28 * 10^(-4)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq(0.0133)/(0.0113)}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq1.18}\bigg )$

From the z tables;

= 0.8809

Let X be the random variation that follows a normal distribution;

Then;

population mean $\mu$ = n × p

population mean $\mu$ = 300 × 0.04

population mean $\mu$ = 12

The standard deviation $\sigma = √(np(1-p))$

The standard deviation $\sigma = √(300 * 0.04(1-0.04))$

The standard deviation $\sigma = √(11.52)$

The standard deviation $\sigma = 3.39$

The z -score can be computed as:

$z = (x - \mu)/(\sigma)$

$z = (16 -12)/(3.39)$

$z = (4)/(3.39)$

z = 1.18

The required probability is:

P(X ≤ 10) = Pr (z ≤ 1.18)

= 0.8809

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15. In the State of California, there are 25 full-time employees to every 4 part-time employees. If there are 250,000 full-time employees, how many part-time employees are there statewide?

Answers

40,000
I know it's not the mathematical way, but it's the same ratio, so just add the same amount of zeroes.

Final answer:

To find the number of part-time employees in California, set up a proportion and solve for x.

Explanation:

To find the number of part-time employees statewide, we can set up a proportion using the given information. We know that there are 25 full-time employees for every 4 part-time employees. So, we can write the proportion as:

25 full-time employees / 4 part-time employees = 250,000 full-time employees / x part-time employees

Cross-multiplying, we get:

25x = 4 * 250,000

Simplifying, we have:

25x = 1,000,000

Dividing both sides by 25, we find:

x = 40,000

Therefore, there are 40,000 part-time employees statewide in California.

Learn more about Calculating number of part-time employees here:

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Form a polynomial f(x) with real coefficients having the given degree and zeros.Degree 4; zeros: 1, multiplicity 2; 2i

Answers

Answer:

Step-by-step explanation:no

A quality control inspector has drawn a sample of 15 light bulbs from a recent production lot. Suppose that 60% of the bulbs in the lot are defective. What is the expected value of the number of defective bulbs in the sample