Mathematics, 01.04.2020 16:55 CameronVand21

You have a really annoying stapler that seems to randomly jam. On any given attempt to staple, it seems to independently jam 10.9% of the time. a) Out of 260 papers stapled, what is the probability that your stapler will jam less than 23 times? Round your answer to 4 decimals.

Answers: 3

Show answers

Answers

Answer from: jazzilove710

0.1230 = 12.30% probability that your stapler will jam less than 23 times

Step-by-step explanation:

I am going to use the normal approximation to the binomial distribution to solve this question.

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 = 0.109, n = 260

$\mu = E(X) = np = 260*0.109 = 28.34$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{260*0.109*0.891} = 5.025$

Out of 260 papers stapled, what is the probability that your stapler will jam less than 23 times?

This is P(X < 23).

Using continuity correction, this is P(X < 23-0.5) = P(X < 22.5), which is the pvalue of Z when X = 22.5. So

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

$Z = \frac{22.5 - 28.34}{5.025}$

Z = -1.16

Z = -1.16 has a pvalue of 0.1230

0.1230 = 12.30% probability that your stapler will jam less than 23 times

Answer from: Quest

step-by-step explanation:

Answer from: Quest

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100 * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

= $25.99 - $6.49

=$19.5

total amount to be paid = $19.5

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 20:30, amandaaaa13

Asmall business produces and sells balls. the fixed costs are $20 and each ball costs $4.32 to produce. each ball sells for $8.32. write the equations for the total cost, c, and the revenue, r, then use the graphing method to determine how many balls must be sold to break even.

Answers: 1

continue

Mathematics, 21.06.2019 21:30, sassy11111515

Cal's go cart has a gas tank with the dimensions shown below. he uses a gas can that holds 11 gallon of gas, to fill the go cart tank. 11 gallon = 231 inches^3 how many full gas cans will it take to fill the go cart's gas tank?

Answers: 3

continue

Mathematics, 22.06.2019 00:00, johnisawesome999

Mrs. blake's bill at a restaurant is $42.75. she wants to leave the waiter an 18% tip. how much will she pay in all, including the tip?

Answers: 2

continue

Mathematics, 22.06.2019 00:00, AnonymousLizard52303

The probability that a tutor will see 0, 1, 2, 3, or 4 students is given below determine the probability distribution's missing value.

Answers: 1

continue

You know the right answer?

You have a really annoying stapler that seems to randomly jam. On any given attempt to staple, it se...