Use the figure at the right for Exercises 1-3. - Can anyone help me pleaseee?

If XX is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases:

Liula [17]

Answer:

(a) The mean, variance and standard deviation of X are 1.60, 0.96 and 0.98 respectively.

(b) The mean, variance and standard deviation of X are 3.20, 0.64 and 0.80 respectively.

(c) The mean, variance and standard deviation of X are 1.50, 0.75 and 0.87 respectively.

(d) The mean, variance and standard deviation of X are 4.00, 0.80 and 0.89 respectively.

Step-by-step explanation:

The random variable X follows a Binomial distribution with parameters n and p.

The mean, variance and standard deviation of X are:

$\mu=np\\\sigma^{2}=np(1-p)\\\sigma=\sqrt{np(1-p)}$

(a)

For n = 4 and p = 0.40 compute the mean, variance and standard deviation of X as follows:

$\mu=np=4\times0.40=1.60\\\sigma^{2}=np(1-p)=4\times0.40\times(1-0.40)=0.96\\\sigma=\sqrt{np(1-p)}=\sqrt{0.96}=0.98$

Thus, the mean, variance and standard deviation of X are 1.60, 0.96 and 0.98 respectively.

(b)

For n = 4 and p = 0.80 compute the mean, variance and standard deviation of X as follows:

$\mu=np=4\times0.80=3.20\\\sigma^{2}=np(1-p)=4\times0.80\times(1-0.80)=0.64\\\sigma=\sqrt{np(1-p)}=\sqrt{0.64}=0.80$

Thus, the mean, variance and standard deviation of X are 3.20, 0.64 and 0.80 respectively.

(c)

For n = 3 and p = 0.50 compute the mean, variance and standard deviation of X as follows:

$\mu=np=3\times0.50=1.50\\\sigma^{2}=np(1-p)=3\times0.50\times(1-0.50)=0.75\\\sigma=\sqrt{np(1-p)}=\sqrt{0.75}=0.87$

Thus, the mean, variance and standard deviation of X are 1.50, 0.75 and 0.87 respectively.

(d)

For n = 5 and p = 0.80 compute the mean, variance and standard deviation of X as follows:

$\mu=np=5\times0.80=4.00\\\sigma^{2}=np(1-p)=5\times0.80\times(1-0.80)=0.80\\\sigma=\sqrt{np(1-p)}=\sqrt{0.80}=0.89$

Thus, the mean, variance and standard deviation of X are 4.00, 0.80 and 0.89 respectively.

6 0

3 years ago

Aleena has a 1-gallon watering can that is full of water.She uses 3/8gallon to water her roses and 1/3gallon to water her gerani

beks73 [17]

Answer:

The answer to your question is 17/24 gallon

Step-by-step explanation:

Data

total volume = 1 gallon

She uses 3/8 gallon and 1/3 gallon

Process

1.- To find the answer, just sum up the water she used to water her roses and the volume she used to water her geraniums.

3/8 + 1/3 =

- Look for the Least common factor

8 x 3 = 24 LCF = 24

- Solve the fraction

3/8 + 1/3 = (9 + 8) / 24

= 17/24

2.- Conclusion

She used 17/24 gallon to water her flowers.

8 0

4 years ago

Read 2 more answers

Help!! 10 pts and brainliest!

o-na [289]

Answer:

6

Step-by-step explanation:

scale factor is 0.25

so

∴ x = 1.5 ÷ 0.25 = 6

5 0

3 years ago

Armando graphed the relationship between temperature and elevation for several cities. The x-coordinate is the elevation in mete

Brums [2.3K]

Quadrant III

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7 0

3 years ago

Help please? Thank youu

melomori [17]

The 3rd choice is the right answer here
Hope this helps :)
Have a wonderful day !

3 0

4 years ago