Hello to any kind and wise soul(s) who might be able to help me with this problem!
My question involves this the Central Limit Theorem- and what do I do with the age 20 in this problem? I'm sure I need to enter this into my equation, but I'm just not sure how or where.
Here's the problem...
According to the NCHS (National Center for Health Statistics), the average height of men over the age of 20 is 69.1 inches with a standard deviation of 5.3 inches. Assume the population distribution is normal.
a. What is the probability that a single randomly selected individual man will be shorter than 69 inches?
b. What is the probability that the mean height of 19 randomly selected men will be shorter than 69 inches?
Here's how I came about my wrong answers:
a. n= 1 x= 69 sigma= 5.3 mu= 69.1
Z= x - mu / (sigma/ quare root of n) So...
Z = 69 - 69.1 / (5.3 / 1) = -.0189 = .4286 or 43%
And I did the same process for b., but n = 19.
What did I do wrong? Thanks so much to whoever can help!