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
Look at this table:<br><br> Is this relation a function?<br> Yes or no
Karo-lina-s [1.5K]

Answer:

no

Step-by-step explanation:

Because the x value isnt repeating

7 0
2 years ago
What is the volume of this container?
Keith_Richards [23]

Answer:

The volume of the container is 56\ in^{3}

Step-by-step explanation:

we know that

The volume of the figure is equal to

V=Bh

where

B is the area of the base

h is the height of the figure

Let

h=4\ in

Find the area of the base B

B=(4*4)-(1*2)=14\ in^{2}

substitute

V=14*4=56\ in^{3}


3 0
3 years ago
What is the probability that a passenger prefers to sit in front of the plane and prefers a window seat
Ksenya-84 [330]

Answer:

A

Step-by-step explanation:

This is a probability question.

We want to calculate the probability that a passenger prefers to sit in front of the plane and at a window seat.

The answer here is directly obtainable from the table. Let’s take a look at that point where we have the front and window merging. We can see that the figure here is 8

Thus, the probability that we want to calculate is this figure over the total = 8/36

= 2/9

6 0
3 years ago
Read 2 more answers
Which of the following are factors of 12?<br><br> 1 And 12<br><br> 2 And 6<br><br> 3 And 4
Phoenix [80]

Answer:

id just learned this a month ago so i think its 2 and 6 i hope u get 100!

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
PLEASE HELP!!!!!!BEST ANSWER = BRAINLIEST!!!
geniusboy [140]
Here is the answers to these questions ...
1. B
2. A
3.42
7 0
3 years ago
Read 2 more answers
Other questions:
  • 12y+d=−19y+t does anyone know the answer
    6·1 answer
  • Simplifying Algebraic Expressions ; 7+9(-6+8)
    7·1 answer
  • Plz help me ............
    9·2 answers
  • What is X plus 11 equals 15
    10·2 answers
  • Solve (6 1/6 -2 5/6)x3
    8·1 answer
  • Please show what you did to find the answer thank you!
    10·1 answer
  • Which expression is equivalent to 64 − 9x2?
    7·1 answer
  • Four interior angles of a pentagon measure 88°, 118, 132, and 100°. What is the measure of the fifth interior angle?
    8·2 answers
  • Find the population variance of: 4 6 8 9 9 <br><br> round to the nearest hundredth
    10·1 answer
  • Given that ​3x^2-3x+2 find each of the following. ​a) ​g(0) ​b) ​g(​) ​c) ​g(​) ​d) ​g(​x) ​e) ​g(1​t)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!