Answer:
(a)

(b)


Step-by-step explanation:
Given

Solving (a): The pmf
This means that we list out the probability of each value of x.
To do this, we simply subtract the current probability value from the next.
So, we have:

The calculation is as follows:





The x values are gotten by considering where the equality sign is in each range.
means 
means 
means 
means 
means 
Solving (b):

This is calculated as:

From the given function


So:



This is calculated as:




Using the normal distribution, it is found that 63.18% of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:

- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The area within 0.9 standard deviations of the mean is the <u>p-value of Z = 0.9(0.8159) subtracted by the p-value of Z = -0.9(0.1841)</u>, hence:
0.8159 - 0.1841 = 0.6318 = 63.18%.
More can be learned about the normal distribution at brainly.com/question/4079902
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Answer: Larger the MAD tells us that the ages of swimmer are far from the mean age. Thus means is not a relevant indicator for the data.
Step-by-step explanation:
We know that the mean absolute deviation (MAD) helps to know whether the mean of a data is a worthy indicator for the data values .
The larger the MAD tells us the values are spread out far from the mean .
Also, larger the MAD makes the mean less worthy as an indicator of the data elements within the data set.
Answer: QN = 12
Step-by-step explanation: This quadrilateral is a paralelogram because its 2 opposite sides (NP and MQ) are parallel and the other 2 (MN and PQ) are congruent.
In paralelogram, diagonals bisect each other, which means QR = RN.
If QR = RN:
QR = 6
Then,
QN = QR + RN
QN = 6 + 6
QN = 12
<u>The diagonal QN of quadrilateral MNPQ is </u><u>QN = 12</u><u>.</u>
It would bw 12 99/100 and then 1299/100