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
What is the value of x? 1/3x-2/3=-18 ( please help it’s due tomorrow)
Nikolay [14]
X=56 is the answer :)
4 0
3 years ago
CAN SOMEONE PLEASE HELP ME OUT PLEASE I WOULD APPRECIATE IT VERY MUCH
tatyana61 [14]

Answer:Decreasing

Step-by-step explanation:

Focus only on the 8-10 interval for x. Note that for x=8 , y=1, for x=9, y=0 and for x=10, y=-1. Y is obviously decreasing for 8 .

6 0
3 years ago
I need help :( the question is hard can you explain and show your work ty
Anika [276]
20%
step by step explanation
3 0
3 years ago
Read 2 more answers
Can someone explain how to solve this?
Fiesta28 [93]

-3*0 is 0-4 is -4 which is less than -2

-3*3 is -9-4 is -13 which is also less than 2

4 0
3 years ago
Read 2 more answers
PLEASE HELP ASAP WILL MARK THE BRAINLEST DUE TODAY NEED YA'LL HELP
tangare [24]

Answer:

nitrogen

Step-by-step explanation:

By far, the most abundant gas in the Earth's atmosphere is nitrogen, which accounts for about 78% of the mass of dry air. Oxygen is the next most abundant gas, present at levels of 20 to 21%

3 0
3 years ago
Read 2 more answers
Other questions:
  • A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.
    5·2 answers
  • Solve the following inequality and graph the solution set on the number line 2(x-3)-5x&lt;9
    11·1 answer
  • Which of the following quadratic regression equations best fits the data shown below?
    11·1 answer
  • Convert the number to scientific notation<br><br> 86,002,300 = .... x 10 to what power
    10·2 answers
  • Sides $\overline{AH}$ and $\overline{CD}$ of regular octagon $ABCDEFGH$ are extended to meet at point $P$. What is the degree me
    11·2 answers
  • Highschool Seniors - What is some advice you can give me for time management, homework and schoolwise? I am a high school freshm
    5·1 answer
  • Which is the best estimate for the percent equivalent of 7/15
    5·2 answers
  • Worth 12 points and please actually help me
    9·2 answers
  • Can someone help me please?
    8·1 answer
  • please help! i can't find the answer on brainly because its a multi step problem but here are the screenshots, please help (70 p
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!