Assume the mean height of soldiers to be 68.22 inches with a variance of 10.8 inches. How many soldiers in a regiment of 1000 would you expect to be below 5.53 feet. The heights are assumed to be normally distributed.
You can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
To find the number of soldiers you would expect to be below 5.53 feet, we need to first convert 5.53 feet to inches. Since 1 foot is equal to 12 inches, 5.53 feet is equal to 12 * 5.53 = 66.36 inches.
Given that the mean height of soldiers is 68.22 inches, and the heights are normally distributed, we need to calculate the z-score for 66.36 inches using the formula:
z = (x - μ) / σ
where:
x is the given value (66.36 inches),
μ is the mean height (68.22 inches), and
σ is the standard deviation (square root of variance = √10.8 inches).
Using the given values, we can calculate the z-score:
z = (66.36 - 68.22) / √10.8
Now we can use a standard normal distribution table or a statistical calculator to find the probability of a z-score being less than or equal to the calculated value. This probability represents the proportion of soldiers that should have a height below 66.36 inches.
Let's assume that probability is P(z ≤ z-score).
To find the expected number of soldiers below 5.53 feet from a regiment of 1000, we multiply the proportion (P) by the total number of soldiers (1000):
Expected number = P * 1000
Note: Since this is an estimation, the expected number may not be an integer.
Using the above steps, you should be able to calculate the expected number of soldiers below 5.53 feet in a regiment of 1000.