Question

Finding Probability Using a Normal Distribution

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3537 grams and a variance of 285,156. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4172 grams. Round your answer to four decimal places.

Answer 1

Been a while since I took stat, but I think this is a z-score problem

Answer 2

Yes it is i need help desperately

Answer 3

Fundamental probability theory states:
\[P_{\chi}(\chi \le x) = F_{\chi}(x)\]In this question \(\chi\) is distributed as a normal distribution with \(\mu = 3537\) and \(\sigma^2 = 285,156\).
\(F_{\chi}(x)\) is the cumulative distribution function of \(\chi\), i.e. normalcdf.

Answer 4

So how do i do it?

Answer 5

So how do i do it?

Answer 6

Use a statistical calculator, Excel, wolfram alpha, etc. and use the cumulative distribution function for normal distribution (normalcdf) with given values for parameters x, \(\mu\) \(\sigma\).

Answer 7

I dont understand what u just said at all

Answer 8

I dont understand what u just said at all

Answer 9

How do i find the standard deviation?

Answer 10

Use this: http://www.danielsoper.com/statcalc3/calc.aspx?id=53
Mean = \(\mu\) = 3537
Standard deviation = \(\sqrt{variance}\) = \(\sqrt{\sigma^2}\) = \(\sigma\) = \(\sqrt{285,156}\)
x = 4172

Answer 11

Im sorry i still dont understand. I dont get that calculator. There isnt a a place for me to put the variance in

Answer 12

or is the variance the standard deviation?

Answer 13

standard deviation = \(\sqrt{variance}\)