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
Elza [17]
2 years ago
7

A filling machine fills bottles of nail polish with amounts that are normallydistributed with mean 18 mL and standard deviation

0.6 mL. A random sample of 12 bottles of this nail polish is selected for inspection.
Required:
a. What is the probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish?
b. What is the probability that the average fill of the twelve bottles is more than 17.5mL?
Mathematics
1 answer:
natulia [17]2 years ago
4 0

Answer:

a. 0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish

b. 0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 18 mL and standard deviation 0.6 mL.

This means that \mu = 18, \sigma = 0.6

a. What is the probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish?

This is the p-value of Z when X = 17.5. So

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

Z = \frac{17.5 - 18}{0.6}

Z = -0.83

Z = -0.83 has a p-value of 0.2033

0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish.

b. What is the probability that the average fill of the twelve bottles is more than 17.5mL?

Twelve bottles, so now n = 12, s = \frac{0.6}{\sqrt{12}}

The probability is:

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

By the Central Limit Theorem

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

Z = \frac{17.5 - 18}{\frac{0.6}{\sqrt{12}}}

Z = -2.89

Z = -2.89 has a p-value of 0.0019

0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL

You might be interested in
The winning average speed for the 2014 Daytona 500 was recorded at 145.29 miles per hour which is a correct description of 145.2
vichka [17]
Just answered this one. It was D.
4 0
3 years ago
Paul Smith pays $50.00 a month for group health insurance. There is a $300 deductible. His medical bills for the last year were
sergiy2304 [10]

Answer:

$1,360

Step-by-step explanation:

Take the monthly payment of $50 and multiply it by 12 because there is 12 months in a year which is $600. Next subtract $2,600 by your deduction of $300 which is $2,300. Then multiply by 20% because the insurance pays 80% leaving you with 20%, you get $460. Add $460 and $300 because those are the amounts you paid and you get $760. Now add the $600 to the $760 because of the monthly payment. The total comes out to $1,360.

7 0
2 years ago
Joe bought a box of laundry detergent that contains 195 scoops each load of laundry uses 2 1/2 scoops how many loads of laundry
Ann [662]

Answer:

Hope this helps

Step-by-step explanation:

5 0
3 years ago
A farmer must decide whether to build a cylindrical grain silo with a radius r, or a rectangular grain silo with a width rand le
Lorico [155]

Answer:

The cylinder has the greater ratio because the ratio for the cylinder is rh/r+2h and the ratio for the rectangular prism is rh/r+3h

Step-by-step explanation:

Just trust me its right

3 0
2 years ago
Th
timama [110]

Answer:

<h2>             b) 10 years</h2>

Step-by-step explanation:

1/20 of 700:  1/20•700 = 35

700 + n•35 = 1050

n•35 = 350

n = 10

8 0
2 years ago
Other questions:
  • Can someone please help me ‍♂️
    12·2 answers
  • How do you subtract an integer from another integer without using
    6·2 answers
  • Factor completely.<br> n^4 - 1
    14·2 answers
  • What is the complete factorization of the polynomial below?<br> x3 + x2 + 4x + 4
    14·1 answer
  • a landscaping store charges 12.50 per pound of gravel if you purchase 3 pounds or less. any gravel you purchase beyond the first
    12·1 answer
  • Page 79 on what should you watch monster movies
    15·2 answers
  • Marcus can choose between a monthly salary of $1,250 plus 4.5% of sales or $2,400 plus 3%
    7·1 answer
  • Jackie has $33, and needs to get a taxi. The cost for a taxi is a fee of $5, plus $7 per mile. Which inequality would help Jacki
    11·1 answer
  • What is the area to this
    7·2 answers
  • Can someone please explain how to do this​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!