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CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars

velikii [3]

Answer:

P(939.6 < X < 972.5) = 0.6469

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 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.

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that $\mu = 965, \sigma = 113$

Sample of 57:

This means that $n = 57, s = \frac{113}{\sqrt{57}} = 14.97$

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

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

By the Central Limit Theorem

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

$Z = \frac{972.5 - 965}{14.97}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915

X = 939.6

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

$Z = \frac{939.6 - 965}{14.97}$

$Z = -1.7$

$Z = -1.7$ has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

So

P(939.6 < X < 972.5) = 0.6469

3 0

2 years ago

A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A prime has coordinates of (–0. 25, 0. 5) after the triangle has

babunello [35]

The true statements about the dilation are as follows;

The scale factor is One-eighth

The coordinates of the C prime are (0.75, 0.5).

The coordinates of B prime are (–0.25, 1).

Given

A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4).

If A prime has coordinates of (–0. 25, 0. 5) after the triangle has been dilated with a center of dilation about the origin.

<h3>What is transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. If an object is transformed then all its points are also transformed. Types of transformation are reflection, dilation, rotation, and translation.

Dilation is the enlargement or reduction in the size of an object. If a point X(x, y) is dilated about the origin by a factor k, its new location is X'(kx, ky).

Triangle ABC with vertices at A(–2, 4), B(–2, 8), and C(6, 4) is dilated to give A'(-0.25, 0.5)

kA = A'

(-2k, 4k) = (-0.25, 0.5)

-2k = -0.25, hence k = 1/8

Therefore the scale factor is 1/8 (one- eight)

The new location of the vertices is B'(-0.25, 1), C'(0.75, 0.5)

To know more about Transformation click the link given below.

brainly.com/question/11709244

3 0

2 years ago

Reports say that the mean birth weight of babies of European heritage is 3.5 kg. Marta wants to perform a significance test to s

Svet_ta [14]

Answer:

what was the answer?

Step-by-step explanation:

8 0

3 years ago

dave is painting a fence in his uncle's yard he painted 2 sections of the fence in 30 minutes Dave has 9 sections to paint. if D

Scrat [10]

Answer:

135

Step-by-step explanation:

30÷2≡15

7 0

2 years ago

A book costs $ 25.00. You have a coupon for 30 % off. Calculate the final price of the book with a 5% GST. (Begin by finding the

guapka [62]

Answer:

$18.375 or rounded = $18.38 (brainliest if correct)

Step-by-step explanation:

25.00- 7.5 = $17.5

5% of 17.5 = 0.875

17.5 +0.875 = 18.375

6 0

2 years ago