Question

Approximately 10% of all people are left-handed. Consider a grouping of fifteen people.

1. State the random variable.
2. Write the probability distribution.
3. Draw a histogram.
4. Describe the shape of the histogram.
5. Find the mean.
6. Find the variance.
7. Find the standard deviation.

Answer 1

a) The number of left handed people out of the 15 people is the random variable here.

b) As all the people left handedness is independent and the probability of being left handed is equal for all, therefore the distribution of the number of left handed people out of 15 people here is given as:

c) The given probability distribution for X is computed in EXCEL first using the BINOM.DIST function as:

Similarly we obtain it for all possible values of X to get the final PMF as:

The histogram of the above values are obtained here as:

d) The shape of the above distribution is called a right skewed distribution as it has a longer tail on the right side of the plot.

e) The mean here is computed as:

Mean = np = 15*0.1 = 1.5

Therefore 1.5 is the required mean of the distribution here.

f) The variance of a binomial distribution is computed as:

Var(X) = np(1-p) = 15*0.1*0.9 = 1.35

Therefore 1.35 is the required variance here.

g) The standard deviation is computed as the square root of variance that is square root of 1.35 which is given as: 1.1619

Therefore 1.1619 is the standard deviation required here.