Question

We have a normal probability distribution for variable x with μ = 24.8 and σ = 3.7. For each of the following, make a pencil sketch of the distribution & your finding. Using 5 decimals,

find: [1] PDF(x = 30); [use NORM.DIST(•,•,•,0)]

Answer 1

To sketch the probability distribution of X, plot the values of X on the horizontal axis and the probabilities on the vertical axis. The mean of X is μ = 24.8 and the standard deviation is σ = 3.7. The probability of more than five people being literate is 0.94989, and it is more likely that four people are literate.

Step-by-step explanation:

Probability Distribution:

To sketch the probability distribution of X, we need to plot the values of X on the horizontal axis and the corresponding probabilities on the vertical axis. Since X follows a normal distribution with a mean of μ = 24.8 and a standard deviation of σ = 3.7, we can use a bell-shaped curve to represent the distribution.

Mean and Standard Deviation:

The mean of X is equal to μ, which is 24.8. The standard deviation of X is equal to σ, which is 3.7.

Probability of More Than Five People Being Literate:

To find the probability that more than five people in the sample are literate, we need to calculate the cumulative probability up to x = 5 and subtract it from 1. Using the NORM.DIST function with the given parameters, the probability is given by 1 - NORM.DIST(5, 24.8, 3.7, 1) =

0.94989