Question

A machine is shut down for repairs if a random sample of 200 items selected from the daily output of the machine reveals at least 15% defectives. (Assume that the daily output has a large number of items.) If on a given day, the machine is producing only 10% defective items, what is the probability that it will be shut down? State and justify a condition that is required to apply a normal approximation to this binomial probability.

Answer #1

The number of defective ones from the sample of 200 items is modelled here as:

The distribution of the proportion here is given as:

The probability that the machine is shutdown is computed here as:

P( p >= 0.15)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

**Therefore 0.0092 is the required probability
here.**

Among 20 metal parts produced in a machine shop, 5 are
defective. If a random sample of three of these metal parts is
selected, find:
The probability that this sample will contain at least two
defectives?
The probability that this sample will contain at most one
defective?

1. A random sample of 15 items is selected from a lot in which
the proportion of defective items is 10%. Find the probability that
the number of defective items in the sample is less than or equal
to 3. (Hint: use the Binomial Distribution Table)
Group of answer choices
a. 0.0556
b. 0.8159
c. 0.9444
d. 0.1841
e. 0.9873
2. A continuous random variable X has a normal
distribution with mean 25. The probability that X takes a
value...

2. Ten percent of the items produced by a machine are defective.
A random sample of 100 items is selected and checked for
defects.
a. Determine the sampling error of the proportion.
b. What is the probability that the sample proportion will
contain more than 13% defective units?
Formulas:
?=?−? ??̅= ? ?̅=? ??̅=√?(?−?) ? √? ? ?

Question 1)
A random sample of 15 items is selected from a lot in which the
proportion of defective items is 10%. Find the probability that the
number of defective items in the sample is less than or equal to
3.
A.
Let X be the cost per gallon of gas at a pump, and
X is normally distributed with mean 2.3 and standard
deviation 0.2. If you fill up at a random gas pump, what is the
probability that...

A random sample is selected from a population with mean μ = 100
and standard deviation σ = 10.
Determine the mean and standard deviation of the x sampling
distribution for each of the following sample sizes. (Round the
answers to three decimal places.)
(a) n = 8 μ = σ =
(b) n = 14 μ = σ =
(c) n = 34 μ = σ =
(d) n = 55 μ = σ =
(f) n = 110...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 11 minutes ago

asked 39 minutes ago

asked 45 minutes ago

asked 45 minutes ago

asked 45 minutes ago

asked 46 minutes ago

asked 53 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago