What number was added to 8 to get a sum of -4?

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

Suppose a dog can run 60 feet in 8 seconds. A cat can run 35 feet in 5 seconds. Which animal can run faster

Alika [10]

60/8 = 7.4. The dog is faster. 35/5 = 7

6 0

3 years ago

How many moles of oxygen are required to burn 3.0 mole of C10H8 (naphthalene)?

astra-53 [7]

Answer: 36 moles oxygen

Step-by-step explanation:

C10H8 + 12O2 ====》 10CO2 + 4H2O

From the equation of the reaction,

1 mole of napth requires 12 moles of O2

3 moles of napth would require x moles O2

X = (3 * 12) / 1

X = 36 moles of oxygen.

Therefore 3 moles of naphtalene (C10H8) would require 36 moles of oxygen

6 0

3 years ago

If you invest $20,000 in a mutual fund averaging 10% compounded monthly, how long will it take to reach $1 million?

antoniya [11.8K]

Answer:

hutghighriughriughriughrihgrighrighirhgrhrgurhuihghruhgiurhirhiughriughriughurhurhugi

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Total Points: 50

Sveta_85 [38]

Answer:

1. slope

2.Positive

3.up and down

4. Left and right

5. 1/1 or over 1 up 1

Step-by-step explanation:

7 0

3 years ago