Question

I need help on C, D, E, F, G, and H. The mean is 27, and the Standard Deviation is 15.01

Answer 1

(a) Mean of the distribution.

The mean of a uniform distribution is

`\begin{gathered} \mu=(a+b)/(2) \\ \mu=(1+53)/(2) \\ \mu=(54)/(2) \\ \mu=27 \\ \\ \text{The mean of the distribution is 27} \end{gathered}`

(b) Standard deviation

The standard deviation is calculated as

`\begin{gathered} \sigma=\frac{b-a}{\sqrt[]{12}} \\ \sigma=\frac{53-1}{\sqrt[]{12}} \\ \sigma=\frac{52}{\sqrt[]{12}} \\ \sigma=15.0111 \end{gathered}`

(c) Probability of Pr( x = 5 )

`\begin{gathered} \text{Since week 1 up to week 53 is uniformly distributed, they have the same probability} \\ \text{all throughout} \\ \\ \text{There are 52 spreads }(53-1) \\ \text{the probability is} \\ \Pr (x=5)=(1)/(52)\approx0.0192 \end{gathered}`

(d) Probability of Pr( 11 < x < 16 )

`\begin{gathered} \Pr (11\le x\le16)=(16-11)/(53-1) \\ \Pr (11\le x\le16)=(5)/(52)\approx0.0962 \end{gathered}`

(e) Probability of Pr( x > 13)

`\begin{gathered} \Pr (x>13)=(53-13)/(52-1) \\ \Pr (x>13)=(40)/(52)\approx0.7692 \end{gathered}`

(f) Probability of Pr ( 18 < x < 42 )

(h) Find the minimum for the lower quartile

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. It starts with the smallest number, for our uniform distribution which starts at week 1, the MINIMUM for the lower quartile is week 1.