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
jolli1 [7]
1 year ago
11

The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 11 mL. Supp

ose that 12 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
What is the distribution of
X
?
X
~ N(
,
)
What is the distribution of
¯
x
?
¯
x
~ N(
,
)
If a single randomly selected individual is observed, find the probability that this person consumes is between 59.3 mL and 61.2 mL.
For the group of 12 pancake eaters, find the probability that the average amount of syrup is between 59.3 mL and 61.2 mL.
For part d), is the assumption that the distribution is normal necessary? YesNo
Mathematics
1 answer:
Whitepunk [10]1 year ago
5 0

Using the normal distribution and the central limit theorem, we have that:

  • The distribution of X is X \approx N(60,11).
  • The distribution of \bar{X} is \bar{X} \approx (60,3.1754).
  • 0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.
  • 0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem, the parameters are given as follows:

\mu = 60, \sigma = 11, n = 12, s = \frac{11}{\sqrt{12}} = 3.1754.

Hence:

  • The distribution of X is X \approx N(60,11).
  • The distribution of \bar{X} is \bar{X} \approx (60,3.1754).

The probabilities are given by the <u>p-value of Z when X = 61.2 subtracted by the p-value of Z when X = 59.3</u>, hence, for a single individual:

X = 61.2:

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

Z = \frac{61.2 - 60}{11}

Z = 0.11

Z = 0.11 has a p-value of 0.5398.

X = 59.3:

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

Z = \frac{59.3 - 60}{11}

Z = -0.06

Z = -0.06 has a p-value of 0.4761.

0.5398 - 0.4761 = 0.0637.

0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.

For the sample of 12, we have that:

X = 61.2:

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

Z = \frac{61.2 - 60}{3.1754}

Z = 0.38

Z = 0.38 has a p-value of 0.6480.

X = 59.3:

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

Z = \frac{59.3 - 60}{3.1754}

Z = -0.22

Z = -0.22 has a p-value of 0.4129.

0.6480 - 0.4129 = 0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.

More can be learned about the normal distribution and the central limit theorem at brainly.com/question/24188986

#SPJ1

You might be interested in
Solve square root <br> (2x+3)^2=36
REY [17]
X=3/2 btw its a fraction
6 0
3 years ago
Read 2 more answers
If you have 63 books and you donate 1/3 of you’re books how many will you have left
ryzh [129]

Answer: 42

Step-by-step explanation: you would do 63 divided by 3 then you would get 21 and do 21×2 and get 42

6 0
3 years ago
SIMPLE CONGRUENCE QUESTION!!! LOTS OF POINTS!
Monica [59]

Answer:

A. Side-Angle-Side (SAS).

Step-by-step explanation:

Sides go first. Side.

Angle next. Angle.

Side again. Side.

You got Side angle side.

7 0
2 years ago
3² x 3 x 3 x 3= <br><br> Simplified into exponential form
ruslelena [56]

Answer:

Step-by-step explanation:

3^{2} *3^{1}*3^{1}*3^{1}

because the bases are all the same.. just add the exponents

3^{2+1+1+1}

or

3^{5}

6 0
2 years ago
Read 2 more answers
A cone has a height of 8 yards and a radius of 3 yards. What is its volume?
alina1380 [7]
<h3>Given:</h3>
  • h= 8 yd
  • r= 3 yd
<h3>Note that:</h3>
  • h= Height
  • r= Radius
<h3>To find:</h3>

The volume of the given cone.

<h3>Solution:</h3>

\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}

\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}

Let's solve!

Substitute the values according to the formula.

V= \frac{1}{3}×3.14×{3}^{2}×8

\large\boxed{V= 75.36 \: {yd}^{3}}

<u>Therefore, the volume of the given cone is 75.36 cubic yards.</u>

7 0
1 year ago
Other questions:
  • The sum of z and 7 algebraic expression
    14·1 answer
  • (18x² – 3x²+x-1) ÷ (x² – 4)​
    15·1 answer
  • PLEASE HELP<br> X=<br> 8<br> 9<br> 10
    12·1 answer
  • The probability that Barry Bonds hits a home run on any given at-bat is 0.16, and each at-bat is independent.
    14·1 answer
  • Which shows two expressions that are equivalent to (Negative 7) (Negative 15) (Negative 5)? (Negative 7) (Negative 75) and (Nega
    8·2 answers
  • You work for a parts manufacturing company and are tasked with exploring the wear lifetime of a certain bearing. You gather data
    9·1 answer
  • 2x+y=3<br>x-y= 1<br><br>solve the equation ​
    6·2 answers
  • A tour bus travels 2,160 miles in 36 hours. What is the average distance the bus travels in one hour?​
    9·1 answer
  • Beth us buying 2.6 pounds of coffee beans. If the coffee costs 6.79 per pound, how much will she pay? Round to the nearest cent.
    10·1 answer
  • A test score in the 3rd percentile would be considered ______. a. about average b. very high c. cannot be determined d. very low
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!