Question

PHSTAT ONLY!!!

Instructions: Show your complete solution. Simply giving the final answer without showing your calculations will NOT merit any points. If you’re using PhStat or Excel calculations, upload the excel file. You can also cut and paste the Excel work output on a word file, and upload it here.

Given a normal distribution with µ = 47 and σ = 6, what is the probability that:

1. X < 39 or X > 44
2. X is between 37 and 46
3. 7% of the values are less than what X value.
4. Between what two X values (symmetrically distributed around the mean) are 70% of the values?

Answer 1

The Excel output is:

The Excel formulas are:

The answer is:

µ	47
σ	6
a.	X < 39 or X > 44		c.	7% of the values are less than what X value.
	x	39			z	-1.48
	z = (x - µ)/σ	-1.33			x = z*σ + µ	38.15
	p-value	0.0912
				d.	Between what two X values (symmetrically distributed around the mean) are 70% of the values?
	x	44			z	-1.04
	z = (x - µ)/σ	-0.5			x = z*σ + µ	40.78
	p-value	0.6915
					z	1.04
	p-value	0.7827			x = z*σ + µ	53.22
b.	X is between 37 and 46
	x	37
	z = (x - µ)/σ	-1.67
	p-value	0.0478
	x	46
	z = (x - µ)/σ	-0.17
	p-value	0.4338
	p-value	0.3860