Mathematics, 18.03.2020 00:08 isaacbrown7one

Suppose 3% of the people contacted by phone are receptive to a certain sales pitch and buy your product. If your sales staff contacts 2000 people, what is the probability that more than 100 of the people contacted will purchase your product?

Answers: 1

Show answers

Answers

Answer from: alessandrotabares

The probability that more than 100 purchase the product is 0

The given parameters are:

$\mathbf{p = 3\%}$

$\mathbf{n = 2000}$

Calculate the mean using

$\mathbf{\mu = np}$

$\mathbf{\mu = 2000 \times 3\%}$

$\mathbf{\mu = 60}$

Calculate the standard deviation using

$\mathbf{\sigma = \sqrt{\mu(1 - p)}}$

So, we have:

$\mathbf{\sigma = \sqrt{60 \times (1 - 3\%)}}$

$\mathbf{\sigma = 7.63}}$

For x = 100, the z-score is calculated using:

$\mathbf{z = \frac{x - \mu}{\sigma}}$

So, we have:

$\mathbf{z = \frac{100 - 60}{7.63}}$

$\mathbf{z = \frac{40}{7.63}}$

$\mathbf{z = 5.24}$

So, the probability that more than 100 purchase the product is calculated using:

$\mathbf{P(x 100) = P(z 5.24)}$

From z-score of probabilities, we have:

$\mathbf{P(x 100) = 0}$

Hence, the probability is 0

Read more about probabilities at:

link

Answer from: christyr2002

0% probability that more than 100 of the people contacted will purchase your product

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

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 samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

p = 0.03, n = 2000

$\mu = E(X) = np = 2000*0.03 = 60$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.03*0.97} = 7.63$

What is the probability that more than 100 of the people contacted will purchase your product?

This is 1 subtracted by the pvalue of Z when X = 100. So

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

$Z = \frac{100 - 60}{7.63}$

Z = 5.24

Z = 5.24 has a pvalue of 1

1 - 1 = 0

0% probability that more than 100 of the people contacted will purchase your product

Answer from: Quest

the circle one

Which graph does not represent a function?

Answer from: Quest

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 13:40

John bought 5 lemons and used 2 of them for a salad how much did he use for.a salad . he used % of the lemons.

Answers: 2

Answer

Mathematics, 21.06.2019 16:30

Anyone know? will mark brainliest if correct

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

Which set of reflections would carry trapezoid abcd onto itself? a) x-axis, y=x, y-axis, x-axis b) x-axis, y-axis, x-axis c) y=x, x-axis, x-axis d) y-axis, x-axis, y-axis, x-axis

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

choose the correct definition for extremo. a. end b. extra c. extract d. eventual

Answers: 2

Answer

You know the right answer?

Suppose 3% of the people contacted by phone are receptive to a certain sales pitch and buy your prod...

Questions

Mathematics, 24.01.2021 03:20

I need help ASAP, marking brainliest! ...