1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Pani-rosa [81]
3 years ago
12

Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that

a given software user will call technical support is 97%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
3 0

Answer:

Since n(1-p) = 3.72 < 10, the normal curve cannot be used as an approximation to the binomial probability.

100% probability that greater than 26 out of 124 software users will call technical support.

Step-by-step explanation:

Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

It is needed that:

np \geq 10 and n(1-p) \geq 10

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

Out of 124 software users

This means that n = 124

Assume the probability that a given software user will call technical support is 97%.

This means that p = 0.97

Conditions:

np = 124*0.97 = 120.28 \geq 10

n(1-p) = 124*0.03 = 3.72 < 10

Since n(1-p) = 3.72 < 10, the normal curve cannot be used as an approximation to the binomial probability.

Consider the probability that greater than 26 out of 124 software users will call technical support.

The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0

1 - 0 = 1

100% probability that greater than 26 out of 124 software users will call technical support.

You might be interested in
!!50 POINTS!! Please answer all, don't just answer to get the points or you'll be reported. And please, do not copy from the int
diamong [38]
G. The shape would be similar since dilation at the origin is just a translation and a translation doesn't affect the shape's size or shape.

h. They will still be similar because adding length to each side will just make the shape larger, and if the shape hasn't changed (which it hasn't) it will remain similar.

I. This is simple, just write an equation of the changes you could do the shape and it would be similar. You would have to explain how many you should move and from which sides (should be all sides). It is better for you to do this because there are millions of possible equations, and if you use the same one then it might be striked.
8 0
3 years ago
Solve the equation and give me how you solved it and the answer
Viktor [21]
Multiplying both sides by 3, we get (3/9)*(2m-16)=(2m+4). Next, we multiply both sides by 9 and expand to get 6x-48=18m+36. Subtracting 6x and 36 from both sides, we get 12x=-48-36=-84. After that, we divide both sides by 12 to get m=-7
4 0
3 years ago
Sean answers 4/5 of the questions on a test correctly. If there are 100 questions, how many did he not answer correctly?
DanielleElmas [232]
He would have answered 20 incorrectly.
3 0
3 years ago
Read 2 more answers
Matt's Mechanics charges $45.95 per hour to do a car repairs plus $30.50 for waste disposal. Write an equation to represent this
katrin2010 [14]

Answer:

45.95x + 30.50

Step-by-step explanation:

<u>Step 1:  Convert words into an expression</u>

Matt's Mechanics charges $45.95 per hour to do a car repairs plus $30.50 for waste disposal.

<em>45.95x + 30.50</em>

<em />

Answer:  45.95x + 30.50

6 0
3 years ago
Read 2 more answers
Choose all that are correct
iren [92.7K]

Answer:

Step-by-step explanation:

The number of defective laptops = 6/145 * 100 as a percent.

The number of defective laptops = 4.13% in a sample of 145

A: False. The percentage should be the same for 290 laptops. The % does not change. The number of defective laptops will change (12)

B: True. It is a reason assertion that about 4% of all laptops will be defective.

C: True. It is not reasonable to assume that only 0.5 laptops will be defective. .5% is too small.

D: True. 10% is too high.

E: False. The variation should not be much.

3 0
2 years ago
Other questions:
  • If a copier contains 60% letter-size paper and 40% legal-size paper, what is the ratio of letter-size paper to legal-size paper?
    12·2 answers
  • HELP...
    5·1 answer
  • If a pizza is cut into twelve pieces and Tommy ate 1/4 of the pizza, how much would be left?
    14·2 answers
  • What is 1 1/25 as a decimal?
    10·2 answers
  • Please explain how to do this I don’t get it!
    7·2 answers
  • Need help solving for X
    15·1 answer
  • Please help ASAP ill give you 20 points and brainly :c
    15·1 answer
  • LOL PLS HELP ME WITH THIS AND EXPLAIN IT , BRIANLY POINTS TO WHOEVER DOES!
    13·1 answer
  • What is the equation of the line? i’m very confused help
    13·1 answer
  • How do you stop a skunk from smelling?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!