-(3x + y) + 2(x

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

At a track meet, 50 people ran the 100-meter dash. 2 people finished in 11 seconds, 5 people finished in 12 seconds, 8 people fi

adoni [48]

You have to do a histogram here:

<span>11 sec: 2 people: probability is 2/50 = 1/25 = 0.04
12 sec: 5 people: probability is 5/50 = 1/10 = 0.1
13 sec: 8 people: probability is 8/50 = 4/25 = 0.16
</span>14 sec: 10 people: probability is 10/50 = 1/5 = 0.2
15 sec: 21 people: probability is 21/50 = 2.38
16 sec: 2 people: probability is 2/50 = 1/25 = 0.04
17 sec: 2 people: probability is 2/50 = 1/25 = 0.04

6 0

2 years ago

Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the g

Bumek [7]

Your parallel equation would be y=-3x-32.

5 0

2 years ago

3 cm 7 cm 4 cm 8 cm area

ryzh [129]

Answer:

672 square inches

with area, multiply the side(s) by themselves for a single number, or their following numbers for more than 2 numbers.

Example

18in x 18in = 324 square inches
4in x 2in x 5in x 9in = 360 square inches

hope this helps!

4 0

1 year ago

What is the average rate of change for this exponential function for the

zhannawk [14.2K]

Answer:

1.5

Step-by-step explanation:

The average rate of change is 1.5

when x=0 , the value of y =1

when x=2 the value of y = 4

<em>average rate of change formula = </em> $\frac{f(b)-f(a)}{b-a}$

a= 0 , f(a)=1

b=2, f(b)= 4

4 - 1 / 2 - 0 = 3/2 = 1.5

6 0

1 year ago

-(3x + y) + 2(x – 4y)?​

-(3x + y) + 2(x – 4y)?