Question

In a shipment of 300 processors, there are 12 defective processors. A quality control consultant randomly collects 6 processors for inspection to determine whether they are defective. Use the Hypergeometric approximation to calculate the following:

a) The probability that there are exactly 2 defectives in the sample

b) The probability that there are at most 5 defectives in the sample, P(X<=5).

## Question 5 Write a script in R to compute the following probabilities of a normal random variable with mean 16 and variance 9

a) lies between 14.4 and 20.3 (inclusive) ```

b) is greater than 21.8 ```

c) is less or equal to 10.5

d) is less than 13 or greater than 19

Answer #1

> #let m=mean and s=standard deiation

> m=16

> s=3

> #a) probabilities lies between 14.4 ad 20.3

> #p(14.4<x<20.3)=p(x<20)-p(x<14.4)

> p=pnorm(20,m,s)-pnorm(14.4,m,s);p

[1] 0.6118874

> #b) probabilities is greater than 21.8

> #p(x>21.8)=1-p(x<21.8)

> p=1-pnorm(21.8,m,s);p

[1] 0.02659757

> #c) probabilities is less than 10.5

> #p(x<10.5)

> p=pnorm(10.5,m,s);p

[1] 0.03337651

> ##b) probabilities is less than 13 or greater than 19

> #p(x<13;x>19)=p(x<13)+p(x>19)

> p=pnorm(13,m,s)+(1-pnorm(19,m,s));p

[1] 0.3173105

>

A quality control department randomly selects 300
motors from a ship and inspects
them for being good or defective. If this sample contains more than
eight defective
motors, the entire shipment is rejected. Assume that 2% of all
motors received are
defective.
a) Find the probability that the given shipment will be
accepted.
b) Find the probability that the given shipment will be
rejected.

5. Suppose a large shipment of compact discs contained 12%
defectives.
If a sample of size 457 is selected, what is the probability
that the sample proportion will differ from the population
proportion by less than 3%? Round your answer to four decimal
places.
11. A researcher believes that 8% of pet dogs in Europe are
Labradors.
If the researcher is right, what is the probability that the
proportion of Labradors in a sample of 644 pet dogs would be...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 13 minutes ago

asked 20 minutes ago

asked 28 minutes ago

asked 30 minutes ago

asked 34 minutes ago

asked 47 minutes ago

asked 49 minutes ago

asked 50 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago