Given Information:
Mean height of children = μ = 41 inches
Standard deviation of height of children = σ = 4 inches
Required Information:
Using Excel find P(x > 34) = ?
Answer:
P(x > 34) = 95.99%
Explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
The Microsoft Excel has a built-in function "NORMDIST" which calculates the probability of a normal distribution.
Syntax:
NORMDIST(x, mean, standard deviation, cumulative flag)
Where x is the variable of interest
Cumulative flag = TRUE or FALSE
The probability that a randomly chosen child is greater than 34 inches tall is given by
P(x > 34) = 1 - P(x < 34)
Using MS Excel,
P(x > 34) = 1 - NORM.DIST(34,41,4,TRUE)
Which return the probability of
P(x > 34) = 1 - 0.040059
P(x > 34) = 0.959941
P(x > 34) = 95.99%
Therefore, there is 95.99% probability that a randomly chosen child is greater than 34 inches tall.
