**Answer:**

a) $430

b) -$90

**Step-by-step explanation:**

Given a random variable X with possible values

with respective probabilities of occurrence

then the expected value E(X) of X is

**a)**

The expected collision payment would then be

0*0.85 + 500*0.04 + 1000*0.04 + 3000*0.03 + 5000*0.02 + 8000*0.01 + 10000*0.01 =** $430**

So the insurance premium that would enable the company to break even is $430

**b)**

<em>The expected value of the collision policy for a policyholder is the expected payments from the company minus the cost of coverage:</em>

$430 - $520 = **-$90**

**Why does the policyholder purchase a collision policy with this expected value?**

Because the policyholder does not know what the probability of having an accident is in her particular case.

Besides, it is better to have the policy and not need it than to need it and not have it.

**Answer:**

0.0668 = 6.68% probability that a student taking the test will score less than 400.

**Step-by-step explanation:**

**Problems of normally distributed samples are solved using the z-score formula.**

In a set with mean and standard deviation , the zscore of a measure X is given by:

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.

**In this problem, we have that:**

**Find the probability that a student taking the test will score less than 400.**

This is the pvalue of Z when X = 400. So

has a pvalue of 0.0668

0.0668 = 6.68% probability that a student taking the test will score less than 400.

20% because 60/300 and x/100 is 60x100 divided by 300 which is 20

The answer is -21p. This is because -7 times 3 is -21 and you multiply the variable to the product to get -21p. Hope this helps!

Answer:

1. -2/3x>8 is x<−12

2. -2/3x <4 is x>−6

Step-by-step explanation: Hope this help :D