Question

Given the following table, answer the questions below.

x | f(x) |

0 | 0.05 |

1 | 0.2 |

2 | 0.3 |

3 | 0.45 |

a) Find the mean of this probability distribution. Round your
answer to one decimal place.

b) Find the standard deviation of this probability distribution.
Give your answer to at least 2 decimal places.

Answer #1

Solution:

x | P(X) | x*P(x) |
x^{2} |
x^{2}* P(x) |

0 | 0.05 | 0 | 0 | 0 |

1 | 0.2 | 0.2 | 1 | 0.2 |

2 | 0.3 | 0.6 | 4 | 1.2 |

3 | 0.45 | 1.35 | 9 | 4.05 |

Sum | 1 | 2.15 | 14 | 5.45 |

a)

Mean = E(X)

= Summation(x.P(X))

= 2.15

**Mean = 2.15**

b)

Now , E(X^{2}) = summation [x^{2} * P(X)] =
5.45

Variance
^{2} = E(X^{2}) - [E(x)]^{2}

= 5.45 - [2.15]^{2}

= 0.8275

Variance
^{2} = 0.8275

Now ,

Standard deviation = = 0.8275= 0.90967026993 = 0.91

**Standard deviation = 0.91**

The probability distribution of a random variable X is
given.
x
−4
−2
0
2
4
p(X =
x)
0.2
0.1
0.3
0.2
0.2
Compute the mean, variance, and standard deviation of
X. (Round your answers to two decimal places.)
Find mean, variance, and standard deviation

x
P(x)
0
0.25
1
0.05
2
0.15
3
0.55
Find the standard deviation of this probability distribution. Give
your answer to at least 2 decimal places

You are given the probability distribution below:
x
0
1
2
3
4
p(x)
0.05
0.35
0.25
0.20
0.15
Determine the standard deviation of X. Report your
answer to three decimal places.

Find the standard deviation of this probability distribution. Give
your answer to at least 2 decimal place
x
P(x)
0
0.3
1
0.05
2
0.3
3
0.35
2.) A manufacturer knows that their items have a normally
distributed lifespan, with a mean of 10.2 years, and standard
deviation of 2.5 years.
If you randomly purchase one item, what is the probability it will
last longer than 9 years?
Round answer to three decimal places

2.The random variable X has the probability distribution table
shown below. Calculate the standard deviation rounded to the four
decimal places.
x −1 0 4 10
P(X = x) 0.2 0.3 0.3 0.2

x
−5
−4
−3
−2
−1
P(X=x)
0.2
0.1
0.3
0.1
0.3
Step 3 of 5 :
Find the standard deviation. Round your answer to one decimal
place.
Step 4 of 5 :
Find the value of P(X> ?5). Round your answer to one decimal
place.
Step 5 of 5 :
Find the value of P(X> ?6). Round your answer to one decimal
place.

Consider the following data:
x
−4
−3
−2
−1
0
P(X=x)P(X=x)
0.3
0.1
0.1
0.2
0.3
Copy Data
Step 2 of 5 :
Find the variance. Round your answer to one decimal place.

Consider the probability distribution shown below.
x
0
1
2
P(x)
0.65
0.30
0.05
Compute the expected value of the distribution.
Compute the standard deviation of the distribution. (Round your
answer to four decimal places.)

Consider the probability distribution shown below.
x 0 1 2
P(x) 0.05 0.20 0.75
Compute the expected value of the distribution.
Compute the standard deviation of the distribution. (Round your
answer to four decimal places.)

Consider the following data:
x 4 5 6 7 8
P(X=x) 0.1 0.2 0.2 0.3 0.2
Step 1 of 5: Find the expected value E(X). Round your answer to
one decimal place.
Step 2 of 5: Find the variance. Round your answer to one decimal
place.
Step 3 of 5: Find the standard deviation. Round your answer to
one decimal place.
Step 4 of 5: Find the value of P(X>4). Round your answer to
one decimal place.
Step 5 of...

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