Basics of ML & AL Week 2 Challenge

2.

Mean or expected value, μ=∑x.P(x)

3.

Skewness is a data characteristic which measures the symmetricity of the curve. It is neither good nor bad for the analysis.

For a normal distribution, the mean, median and mode coincide. However, this is an ideal case and most of the real data have either postive or negative skewness.

A positive skewness indicates that the median and mode are greater than the mean value. On the other hand, for a negatve skewness, the mean value is higher than the median and mode.

4.

a)P(X<711)

P(X<711) = P(680 + 31) = P(μ+1σμ+1σ)

In a normal distribution, the area under the curve on the left, which is the probability of the outcomes, is 0.5

Also, area under the curve from origin to 1σσ is 0.34

Therefore, P(X<711) = 0.5 + 0.34 = 0.84

b)P(X>740)

Value of Z corresponding to X=740,

Z=(X−μ)/σ Z

Z=(740−680)/31=1.935=1.94Z=740-68031=1.935=1.94

Using the Z-table, the probability P(Z<1.94) = 0.97381

c)P(600<x<720)< p=""></x<720)<>

This can be rewritten as P(-2.58<Z<1.29)

P(Z<-2.58) = 0.00494

P(Z<1.29) = 0.90147

P(-2.58<Z<1.29) = P(Z<1.29) - P(Z<-2.58) = 0.90147 - 0.00494 = 0.897

P(600<x<720) =0.897

d)P(X=720)

Z(X=720) = 1.29

For calculating P(Z=1.29), we need to subtract the area on the left as well the right of the curve from the total area.

P(Z=1.29) = 1 - P(Z<1.29) - P(Z>1.29) = 1 - 0.90147 - (1-0.90147) = 0

Therefore, P(X=720) = 0

5.

The area under the curve between the mean and 1 standard deviation is 34.1% of the total area. This means that 34.1% of the outcomes lie in this region.

Also, the area between μ+1σandμ+2σμ+1σandμ+2σ is 13.6% of the total area