Basics of ML & AL Week 2 Challenge

1)Calculate all 4 business moments using pen and paper for the below data set?

2)What is the significance of expected value when simple mean (Sum of all observations/number of observations) is already in place

The expected value is a concept that extends beyond simple mean and provides a deeper understanding of probability and statistical analysis.

While the simple mean calculates the average of a set of observations, the expected value incorporates the probabilities associated with each observation to provide a more comprehensive measure.

3)Having skewness in the curve considered to be bad in the analysis?

Skewness is a measure of the asymmetry of a probability distribution or dataset. It indicates whether the data is skewed to the left (negative skewness) or to the right (positive skewness) relative to the normal distribution, which has zero skewness.

So we can say that Skewness in a data distribution is not necessarily "bad" or negative in analysis.

4)Evaluate the probabilities for continuous normal distribution with given mean = 680 and standard deviation = 31

a)P(X<711)

b)P(X>740)

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

d)P(X=720)

QNo.4

Mean = 680
Standard deviation = 31

z = (x - μ) / σ
z = standard score
x = given value
μ = mean
σ = standard deviation.

a) P(X < 711):
First, we calculate the z-score:
z = (711 - 680) / 31 = 31 / 31 = 1

Using the standard normal distribution table, we find that P(Z < 1) is approximately 0.8413.

Therefore, P(X < 711) = 0.8413.

b) P(X > 740):
Similarly, we calculate the z-score:
z = (740 - 680) / 31 = 60 / 31 = 1.9355

Using the standard normal distribution table, we find that P(Z > 1.9355) is approximately 0.0269.

Therefore, P(X > 740) = 0.0269.

c) P(600 < X < 700):
First, we calculate the z-scores for the lower and upper limits:
Lower z-score:
z_lower = (600 - 680) / 31 = -80 / 31 ≈ -2.5806

Upper z-score:
z_upper = (700 - 680) / 31 = 20 / 31 ≈ 0.6452

Using the standard normal distribution table, we find P(-2.5806 < Z < 0.6452) is approximately 0.7394.

Therefore, P(600 < X < 700) = 0.7394.

d) P(X = 720):
Since the normal distribution is continuous, the probability of X taking a specific value, such as 720, is zero.

Therefore, P(X = 720) = 0.

5)Explain the curve on the right side

34.1% of data is confined within first standard deviation centered around mean =0 and 47.7% of data is centerd around mean=0 and confined within 2nd Standard deviation.