7. - / 8 points determine whether the distribution shown below is a valid probability distribution. (a) is the distribution valid? $\bigcirc$ no, because $\sum p(x)\
eq 0$ $\bigcirc$ yes it is valid because $\sum p(x)=1$ and each $p(x)0$ $\bigcirc$ no, because some values of $x$ are missing $\bigcirc$ no, because $\sum p(x)\
eq 1$ (b) what are the only reasonable values of $x$? (enter your answers from smallest to largest.) (c) what is the probability that $x = 32$? (d) what is the probability that $x = 24$? (e) what is the probability that $x$ is more than 34?

Question

7. - / 8 points determine whether the distribution shown below is a valid probability distribution. (a) is the distribution valid? $\bigcirc$ no, because $\sum p(x)\
eq 0$ $\bigcirc$ yes it is valid because $\sum p(x)=1$ and each $p(x)>0$ $\bigcirc$ no, because some values of $x$ are missing $\bigcirc$ no, because $\sum p(x)\
eq 1$ (b) what are the only reasonable values of $x$? (enter your answers from smallest to largest.) (c) what is the probability that $x = 32$? (d) what is the probability that $x = 24$? (e) what is the probability that $x$ is more than 34?

Accepted Answer

### Part (a)
# Explanation:
## Step1: Recall valid probability distribution conditions
A valid probability distribution requires two conditions: 1) Each $ p(x) > 0 $, and 2) The sum of all $ p(x) $ values is equal to 1.

## Step2: Calculate the sum of $ p(x) $
Sum the given probabilities: $ 0.27 + 0.2 + 0.26 + 0.27 $.
$$
0.27 + 0.2 = 0.47 \
0.47 + 0.26 = 0.73 \
0.73 + 0.27 = 1
$$
Also, each $ p(x) $ (0.27, 0.2, 0.26, 0.27) is greater than 0. So the distribution satisfies both conditions.

# Answer:
Yes it is valid because $\sum p(x)=1$ and each $ p(x)>0$

### Part (b)
# Explanation:
## Step1: Identify reasonable $ x $ values
The reasonable values of $ X $ are the ones listed in the probability distribution table, as these are the values for which we have probabilities defined.

## Step2: Order the $ x $ values
The $ x $ values are 21, 28, 32, 40. Ordering them from smallest to largest: 21, 28, 32, 40.

# Answer:
21, 28, 32, 40

### Part (c)
# Explanation:
## Step1: Find $ p(x) $ for $ x = 32 $
From the table, when $ x = 32 $, the probability $ p(x) $ is given as 0.26.

# Answer:
0.26

### Part (d)
# Explanation:
## Step1: Check for $ x = 24 $ in the table
The table only has $ x $ values 21, 28, 32, 40. There is no entry for $ x = 24 $, so the probability that $ X = 24 $ is 0 (since it's not a defined value in the distribution).

# Answer:
0

### Part (e)
# Explanation:
## Step1: Identify $ x $ values more than 34
The $ x $ values are 21, 28, 32, 40. Values more than 34 is just 40.

## Step2: Find $ p(x) $ for $ x = 40 $
From the table, $ p(40) = 0.27 $. So the probability that $ X $ is more than 34 is $ p(40) = 0.27 $.

# Answer:
0.27

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Part (a)

Step1: Recall valid probability distribution conditions

Step2: Calculate the sum of \( p(x) \)

Step1: Identify reasonable \( x \) values

Step2: Order the \( x \) values

Step1: Find \( p(x) \) for \( x = 32 \)

Answer:

Part (b)