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
Advocard [28]
3 years ago
5

An insurance company has 25,000 automobile policy holders. If the yearly claim of a policy holder is a random variable with mean

320 and standard deviation 540, approximate the probability that the total yearly claim exceeds 8.3 million.
Mathematics
1 answer:
telo118 [61]3 years ago
6 0

Answer:

P(T>8300000)=1-P(T

Step-by-step explanation:

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".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Data given

n = 25000 represent the automobile policy holders

\mu= 320 represent the population mean

\sigma =540 represent the population standard deviation

Let T the variable that represent the total of interest on this case. We can assume that the random variable for an individual policy holder is given by:

X\sim N(\mu = 540, \sigma=540)

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

Solution to the problem

First we need to find the distribution for the random variable T like this:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

And the total T is given by:

T=\sum_{i=1}^n X_i =n \bar X

We can find the expected value, variance and deviation for this random variable like this:

E(T)= n E(\bar X) = n \mu = 25000*320=8000000

Var(T)= Var(n\bar X)= n^2 Var(\bar X) = n^2 \frac{\sigma^2}{n}=n \sigma^2 =25000*(540^2)=7290000000

Sd(T)=\sqrt{7290000000}=85381.497

And we are interested on this probability:

P(T>8300000)

And we can use the Z score formula given by:

Z=\frac{T-E(T)}{\sigma_T}

P(T>8300000)=1-P(T

You might be interested in
On picture day, 3 times as many girls wore dresses rather than pants. If there are 12 girls in the class, how many wore a dress?
katrin2010 [14]

Answer:

36

Step-by-step explanation:

3 * 12 = 36

if there are 12 girls and 3 times more wore dress then 3 times 12 is 36.

3 0
2 years ago
Read 2 more answers
Ice cream jejebbeheue
Effectus [21]

Answer:

Step-by-step explanation:

3 0
3 years ago
Please help<br> What does X=??
Lilit [14]

Answer:

41

Step-by-step explanation:

the 2 triangles are same so the angles would be also same. 180-86-53= 41

6 0
3 years ago
What is the answer??
Lubov Fominskaja [6]

Answer:

<h2>(0, -2)</h2>

Step-by-step explanation:

A(x, y)

rotated 180°: A'(-x, -y)

translated n units:

left (x - n, y)

right (x + n, y)

up (x, y + n)

down (x, y - n)

We have R(-3, 2)

rotated 180°: (-(-3), -2) = (3, -2)

translated 3 units left: (3 - 3, -2) = (0, -2)

7 0
3 years ago
A group of 54 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic
Ket [755]

Answer:

t=\frac{5.25-4.73}{\frac{3.98}{\sqrt{54}}}=0.9601  

P-value  

First we find the degrees of freedom given by:

df = n-1= 54-1=53

Since is a two-sided test the p value would be:  

p_v =2*P(t_{53}>0.9601)=0.3414  

Step-by-step explanation:

Data given and notation  

\bar X=5.25 represent the sample mean

s=3.98 represent the sample standard deviation

n=54 sample size  

\mu_o =4.73 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean differs from 4.73, the system of hypothesis would be:  

Null hypothesis:\mu =4.73  

Alternative hypothesis:\mu \neq 4.73  

Since we know don't the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

t=\frac{5.25-4.73}{\frac{3.98}{\sqrt{54}}}=0.9601  

P-value  

First we find the degrees of freedom given by:

df = n-1= 54-1=53

Since is a two-sided test the p value would be:  

p_v =2*P(t_{53}>0.9601)=0.3414  

7 0
3 years ago
Other questions:
  • What is the factored form of the expression k^2 - 9h^2
    10·1 answer
  • What is the Slope of a line That contains (2,5) and (3, 1) Sketch the graph. Need help with this question.​
    10·1 answer
  • Write the equation of a line with a slope of 3 and a y-intercept of 4
    7·1 answer
  • Determine whether the measures for the figure shown are proportional. A) the length of a side and the perimeter. B) the length o
    12·1 answer
  • Fred wants to but two teeshirt. The first shop sells them for £11.45 each and it is buy one get one half price. The second shop
    13·2 answers
  • Bananas cost $1.10 per pound. How much will five pounds of bananas cost?
    14·2 answers
  • What is the measure of angle 7
    12·1 answer
  • Anna bought 5110
    9·2 answers
  • Image below.<br> Explain
    6·2 answers
  • Please someone help me thanks :D
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!