Mathematics, 14.06.2020 00:57, leannaadrian

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1425 chocolate chips?

Answers: 2

Show answers

Answers

answered: calibaby1220

a) 85.36% probability that a randomly selected bag contains between 1100 and 1500 chocolate chips

b) 16.35% probability that a randomly selected bag contains fewer than 1125 chocolate chips

c) 0.3446 = 34.46% of bags contains more than 1200 chocolate chips

d) 91st percentile.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this question, we have that:

$\mu = 1252, \sigma = 129$

(a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips?

This is the pvalue of Z when X = 1500 subtracted by the pvalue of Z when X = 1100.

X = 1500

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

$Z = \frac{1500 - 1252}{129}$

Z = 1.92

Z = 1.92 has a pvalue of 0.9726

X = 1100

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

$Z = \frac{1100 - 1252}{129}$

Z = -1.18

Z = -1.18 has a pvalue of 0.1190

0.9726 - 0.1190 = 0.8536

85.36% probability that a randomly selected bag contains between 1100 and 1500 chocolate chips

(b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips?

This is the pvalue of Z when X = 1125. So

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

$Z = \frac{1125 - 1252}{129}$

Z = -0.98

Z = -0.98 has a pvalue of 0.1635

16.35% probability that a randomly selected bag contains fewer than 1125 chocolate chips.

This is 1 subtracted by the pvalue of Z when X = 1200.

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

$Z = \frac{1200 - 1252}{129}$

Z = -0.40

Z = -0.40 has a pvalue of 0.3446

0.3446 = 34.46% of bags contains more than 1200 chocolate chips

(d) What is the percentile rank of a bag that contains 1425 chocolate chips?

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

$Z = \frac{1425 - 1252}{129}$

Z = 1.34

Z = 1.34 has a pvalue of 0.91

So the answer is the 91st percentile.

answered: Guest

ik how do do this just give me a few minutes and i will give it to

answered: Guest

6hope this ! ! ’

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 13:30, ilan4225

I'm being volume of cylinder with 13 in. radius and 30 in height answer choices in pic

Answers: 2

continue

Mathematics, 21.06.2019 21:40, dededese2403

Astudy was interested in determining if eating milk chocolate lowered someone's cholesterol levels. ten people's cholesterol was measured. then, each of these individuals were told to eat 100g of milk chocolate every day and to eat as they normally did. after two weeks, their cholesterol levels were measured again. is there evidence to support that their cholesterol levels went down? how should we write the alternative hypothesis? (mud = the population mean difference= before - after)a. ha: mud = 0b. ha: mud > 0c. ha: mud < 0d. ha: mud does not equal 0

Answers: 1

continue

Mathematics, 22.06.2019 00:00, gildedav001

When a 757 passenger jet begins its descent to the ronald reagan national airport in washington, d. c., it is 3900 feet from the ground. its angle of descent is 6 degrees. how far must the plane fly to reach the run way? a. 37,106 ft b. 37,310.4 ft c. 23,456.6 ft d 2,492.7 ft

Answers: 2

continue

Mathematics, 22.06.2019 05:00, u8p4

With this problem-elena cycled to school. find the distance travelled by elena if her bicycle wheels rotated 840 times and the radius is 0.25 m.

Answers: 2

continue

Do you know the correct answer?

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally...