How many rectangular faces does a hexagonal pyramid have?

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

Mekhanik [1.2K]

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.

3 0

3 years ago

What is 52000-53800=? Show work

solmaris [256]

53800
- 52000
-------------
1800

8 0

3 years ago

Explain how to solve 5^(x − 2) = 8 using the change of base formula log base b of y equals log y over log b.

Ray Of Light [21]

Answer:

x = 3.3

Step-by-step explanation:

A equation is given to us and we need to solve out for x. The given equation is ,

Take log on both sides with base as " 10" . We have ,

Simplify using the property of log , , we have ,

Simplify ,

Again simplify using the property of log ,

We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,

Simplify the RHS ,

Add 2 both sides ,

Hence the Value of x is 3.30 .

3 0

2 years ago

What are effective elements to include in introductions? Check all that apply.

dlinn [17]

The effective elements to include in the introductions are statement of the topic, a relevant anecdote and a surprising fact about the topic. Therefore the option 1st, 2nd and 6th options are correct.

<h3>What is Introduction? </h3>

Introduction is the starting line or the opening hook or portion that attracts the readers attention which carries the relevant background of the information.

It is the statement which represents the main point of the following argument or the paragraphs.

There are many elements that included in the introductory part some of them are as follows:-

a statement of the topic
a relevant anecdote or tale
a surprising fact about the topic

Therefore the option 1st, 2nd and 6th options are correct.

Learn more about Introduction here:

brainly.com/question/3964580

#SPJ1

7 0

2 years ago

Read 2 more answers

During the Playoff the schools football team has on average 30% their games than during the regular season. The average for this

exis [7]

Answer:12000

Step-by-step explanation:

During the Playoff the schools football team has on average 30% their games than during the regular season

The average for this year's playoffs attendance was 15,600 fans

To get the number of fans during a regular season goes thus:

Since there is an increase of 30%, we add 100% to 30% which gives:

100% + 30% = 130%

= 15600 ÷ 130%

= 15600 ÷ 130/100

= 15600 × 100/130

= 15600 × 0.7692

= 12000

There are 12000 fans during a regular season

5 0

3 years ago

Read 2 more answers