1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
prisoha [69]
3 years ago
10

The amount of soft drink in a bottle is a Normal random variable. Suppose that in 7% of the bottles containing this soft drink t

here are less than 15.5 ounces, and in 10% of them there are more than 16.3 ounces. What are the mean and standard deviation of the amount of soft drink in a randomly selected bottle
Mathematics
1 answer:
WITCHER [35]3 years ago
6 0

Answer:

The mean is 15.93 ounces and the standard deviation is 0.29 ounces.

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.

7% of the bottles containing this soft drink there are less than 15.5 ounces

This means that when X = 15.5, Z has a pvalue of 0.07. So when X = 15.5, Z = -1.475.

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

-1.475 = \frac{15.5 - \mu}{\sigma}

15.5 - \mu = -1.475\sigma

\mu = 15.5 + 1.475\sigma

10% of them there are more than 16.3 ounces.

This means that when X = 16.3, Z has a pvalue of 1-0.1 = 0.9. So when X = 16.3, Z = 1.28.

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

1.28 = \frac{16.3 - \mu}{\sigma}

16.3 - \mu = 1.28\sigma

\mu = 16.3 – 1.28\sigma

From above

\mu = 15.5 + 1.475\sigma

So

15.5 + 1.475\sigma = 16.3 – 1.28\sigma

2.755\sigma = 0.8

\sigma = \frac{0.8}{2.755}

\sigma = 0.29

The mean is

\mu = 15.5 + 1.475\sigma = 15.5 + 1.475*0.29 = 15.93

The mean is 15.93 ounces and the standard deviation is 0.29 ounces.

You might be interested in
Is √4 rational or irrational?​
Lelu [443]
Rational because you get a whole number
7 0
3 years ago
Find the product mentally.
yaroslaw [1]
(ab+3)(ab−3)

=(ab+3)(ab+−3)

=(ab)(ab)+(ab)(−3)+(3)(ab)+(3)(−3)

=a^2b^2−3ab+3ab−9

=a^2b^2−9

8 0
3 years ago
Read 2 more answers
What percent of a circle is 3/6 of a circle
Vlad1618 [11]
50%
You have half of 6 so the percentage would be half of 100
8 0
3 years ago
Read 2 more answers
Scientific Notation is made up of two number parts. The second part is a power of base 10.
Aneli [31]

Answer:

Step-by-step explanation:

True

7 0
3 years ago
Pls helpppppp i begggg​
Artist 52 [7]

Answer

x Is less than 4

Step-by-step explanation:

It will be an open circle and the arrow is going the left direction on the number 4

8 0
2 years ago
Other questions:
  • Definition: Moving a figure around a fixed point in the plane is called making a
    15·1 answer
  • Help asap please guys​
    6·1 answer
  • Given the following formula solve for x2
    8·1 answer
  • PLEASE HELP!! !:((( Which value for x makes the sentence true?
    15·1 answer
  • A hand of six integer cards has one matching set of two or more cards. If the matching set of cards is removed from the hand, th
    9·1 answer
  • jan typically earns $435 each week of which 78.30 withheld for taxes. what percent of jan's earnings are withheld each week solv
    6·1 answer
  • What is the constant term this equation
    9·1 answer
  • PLEASEEE HELP MEEEE!!
    6·2 answers
  • -9y + 8(4z + 3y) -6x <br><br><br> PLZ HELP
    10·2 answers
  • NEED HELP ASAP WILL GIVE BRAINLIEST
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!