Solve for x round to the nearest degree if necessary

A sample of 100 cars driving on a freeway during a morning commute was drawn, and the number of occupants in each car was record

makkiz [27]

Answer:

$E(X)=1*0.74 +2*0.1 +3*0.11+ 4*0.03 +5*0.02=1.49$

$Var(X)=E(X^2)-[E(X)]^2 =3.11-(1.49)^2 =0.8899$

$Sd(X)=\sqrt{Var(X)}=\sqrt{0.8899}=0.943$

Step-by-step explanation:

For this case we have the following data given:

X 1 2 3 4 5

F 74 10 11 3 2

The total number of values are 100, so then we can find the empirical probability dividing the frequency by 100 and we got the followin distribution:

X 1 2 3 4 5

P(X) 0.74 0.10 0.11 0.03 0.02

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.

Solution to the problem

In order to calculate the expected value we can use the following formula:

$E(X)=\sum_{i=1}^n X_i P(X_i)$

And if we use the values obtained we got:

$E(X)=1*0.74 +2*0.1 +3*0.11+ 4*0.03 +5*0.02=1.49$

In order to find the standard deviation we need to find first the second moment, given by :

$E(X^2)=\sum_{i=1}^n X^2_i P(X_i)$

And using the formula we got:

$E(X^2)=1^2 *0.74 +2^2 *0.1 +3^2 *0.11 +4^2 0.03 +5^2 *0.02=3.11$

Then we can find the variance with the following formula:

$Var(X)=E(X^2)-[E(X)]^2 =3.11-(1.49)^2 =0.8899$

And then the standard deviation would be given by:

$Sd(X)=\sqrt{Var(X)}=\sqrt{0.8899}=0.943$

7 0

3 years ago

It takes Doug 3 days to reroof a house. If Doug's son helps him, the job can be completed in 2 days. How long would it take Doug

cestrela7 [59]

The answer is 1 day because if it takes Doug 3 days by himself and if his son helps him and it takes 2 days with the both of them that means it would only take Doug's son 1 day.

5 0

4 years ago

Suppose two chemicals are reacted together. It takes 1000 kJ of energy to break the bonds of the reactants and 850 kJ of energy

dlinn [17]

B i think is is 150kj

3 0

3 years ago

Read 2 more answers

HALP <br>find the x and y to the following 2x-3y=5 and x+2y=-1

dusya [7]

Answer:

x=1, y=-1. (1, -1)

Step-by-step explanation:

2x-3y=5

x+2y=-1

---------------

2x-3y=5

-2(x+2y)=-2(-1)

-----------------------

2x-3y=5

-2x-4y=2

-------------

-7y=7

y=7/-7

y=-1

x+2(-1)=-1

x-2=-1

x=-1+2

x=1

7 0

3 years ago

According to the Sleep Foundation, the average night’s sleep is 6.8 hours. Assume the standard deviation is .6 hours and that th

Ivan

Answer:

9.18% probability that a randomly selected person sleeps 6 hours or less

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 6.8, \sigma = 0.6$

What is the probability that a randomly selected person sleeps 6 hours or less?

This is the pvalue of Z when X = 6. So

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

$Z = \frac{6 - 6.8}{0.6}$

$Z = -1.33$

$Z = -1.33$ has a pvalue of 0.0918

9.18% probability that a randomly selected person sleeps 6 hours or less

5 0

3 years ago