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
avanturin [10]
3 years ago
5

The amount of potato chips an 18-ounce bag contains follows a normal distribution with a mean of 18.5 ounces and a standard devi

ation of 0.2 ounces. 100 bags of chips were randomly selected. What is the probability that the sample mean weight of these 100 bags is less than 18.6 ounces
Mathematics
1 answer:
bekas [8.4K]3 years ago
7 0

Answer:

100% probability that the sample mean weight of these 100 bags is less than 18.6 ounces

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 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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

\mu = 18.5, \sigma = 0.2, n = 100, s = \frac{0.2}{\sqrt{100}} = 0.02

What is the probability that the sample mean weight of these 100 bags is less than 18.6 ounces

This is the pvalue of Z when X = 18.6. So

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

By the Central Limit Theorem

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

Z = \frac{18.6 - 18.5}{0.02}

Z = 5 has a pvalue of 1

100% probability that the sample mean weight of these 100 bags is less than 18.6 ounces

You might be interested in
How can you write an equation for a line from one point and the slope?
Andrew [12]

Answer y=mx+b


Step-by-step explanation: b is the y intercept and x is the slope


5 0
3 years ago
Three-fourths was subtracted from a number, and then 5/4 was added to the result. The sum was -7.
Rasek [7]

Hi there!

Let's start by replacing "a number" by the letter "x" so that we can do an equation and isolate "x" to find your answer :

(x - \frac{3}{4}) + \frac{5}{4} = -7

subtract \frac{5}{4} on each side of the equation


x - \frac{3}{4} = -8.25

add \frac{3}{4} on each side of the equation

x = -7.5


-7.5 - 3/4 = -8.25

-8.25 + 5/4 = <u>-7</u>


So your answer is : Three-fourths was subtracted from -7.5, and then 5/4 was added to the result. The sum was -7.


There you go! I really hope this helped, if there's anything just let me know! :)



7 0
3 years ago
Which set of numbers does -5 belong ​
tester [92]
Is there any more to this question? Because-5 doesn’t belong anywhere
3 0
3 years ago
What is the solution to -2(8×-4)&lt;2x+5
Monica [59]
Distribute the -2 to get 

-16x + 8 < 2x + 5

3 < 18x 

1/6 < x

so x > 1/6
7 0
3 years ago
Factorize 12x² + 15xy​
kolezko [41]

Answer:

3x(4x+5y)

Step-by-step explanation:

and yh.........

4 0
3 years ago
Read 2 more answers
Other questions:
  • Karen is 6 yrs older than her sister Michelle and Michelle is two years younger than their brother David If the sum of their age
    14·1 answer
  • What do the common factors of 120 and 150 represent?
    13·1 answer
  • Write 7 and 4/5ths as a decimal.
    12·1 answer
  • Franks credit card has no annual fee, 23.99% interest rate. Switch to new card 16.99% rate. $35 annual fee. How much average bal
    9·1 answer
  • Which one is correct?
    9·2 answers
  • Determine the decision criterion for rejecting the null hypothesis in the given hypothesis​ test; i.e., describe the values of t
    11·1 answer
  • Solve the system of equations algebraically:<br><br> y = x+5<br> y = -2x
    9·2 answers
  • There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2
    12·1 answer
  • If x=5y-1and 3x+5=-32, what is the value of y
    9·1 answer
  • Fifty 11th graders were asked to select a favorite pattern out of 6 choices.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!