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
poizon [28]
3 years ago
7

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104 inches, and a standard

deviation of 14 inches. What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches
Mathematics
1 answer:
dsp733 years ago
8 0

Answer:

91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

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 random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 104, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2

What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

This is the pvalue of Z when X = 106.8. So

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

By the Central Limit Theorem

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

Z = \frac{106.8 - 104}{2}

Z = 1.4

Z = 1.4 has a pvalue of 0.9192

0.9192 = 91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

You might be interested in
I'm confused on this<br>(this is 12 year old math) ​
Gemiola [76]

Answer: the top box can be the linear equation y=40x+15 and the bottom box is 40

Step-by-step explanation:

If you swim 15 more minutes than your friend and your swam 55 minutes, that means your friend only swam 40 minutes. The set amount of time that your friend swims for <em>x</em> is 40 minutes. So the additional time you swim is <em>b</em>, 15 minutes.

7 0
2 years ago
Classify the solid figure.
kap26 [50]
That looks like a rectangular prism
8 0
3 years ago
Read 2 more answers
What unfortunate mistake did the champion ice skater make with his gold medal
Fed [463]

Answer:

He Had It Bronzed

Step-by-step explanation:

Hope this help pls mark as brainlest!!

5 0
3 years ago
The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people.
NISA [10]

Answer:

8.2-2.58\frac{2.2}{\sqrt{18}}=6.86    

8.2+2.58\frac{2.2}{\sqrt{18}}=9.54    

So on this case the 90% confidence interval would be given by (6.86;9.54)    And the error is given by:

ME= 2.58\frac{2.2}{\sqrt{18}} =1.338

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X=8.2 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=2.2 represent the population standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

Now we have everything in order to replace into formula (1):

8.2-2.58\frac{2.2}{\sqrt{18}}=6.86    

8.2+2.58\frac{2.2}{\sqrt{18}}=9.54    

So on this case the 90% confidence interval would be given by (6.86;9.54)    And the error is given by:

ME= 2.58\frac{2.2}{\sqrt{18}} =1.338

8 0
3 years ago
Read 2 more answers
At the city museum, child admission is $6.20 and adult admission is $9.50. On Friday, tickets were sold for a total sales of $10
Nostrana [21]

Answer:

98child tickets were sold that day

Step by step Explanation:

Let the number of children= A of the number of adult

Then

6.20C + 9.50A = 1082.0

From the question it was said that four times as many adult tickets as child tickets were sold which implies that number of adult was FOUR times the children, then we can say

A= 4C

Then substitute into the above equation

6.20C + 9.50A = 1082.0

6.20C + 9.50(4C) = 1082.0

6.20C + 38C= 1082.0

44.2C =1082.0

C= 24.48

But we know that

A= 4C

A=4* 24.48

A= 97.9

Therefore ,98child tickets were sold that day

6 0
3 years ago
Other questions:
  • All my points and BRAINLIEST!!!!<br><br> Please help
    5·2 answers
  • A number cube numbered 1 - 6 is rolled once. What is the probability that the side facing up shows 4
    14·2 answers
  • Hey I don't understand but I provided the formula which you could help the 8 is the r the 2 is the h solve for me thanks
    8·1 answer
  • When two musical notes are a “sixth” apart, the frequency of the lower note is 3/5 the frequency of the higher note. Using f as
    9·1 answer
  • Graph: f(x) = x + 3
    13·1 answer
  • Katie has read 32% of a book. if she has read 80 pages, how many more pages does Katie have left to read?
    5·1 answer
  • an athlete is running around a circular path that has a diameter of 250 and an arc of 120 also use 3.14 as pie
    11·1 answer
  • Solve super fast please
    10·1 answer
  • What's 8÷5/9? I give brainliest &lt;3​
    14·2 answers
  • 8a+3.28=46.28<br> solve for a please ik I already asked but I need to pass this test thank you :)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!