A population of values has a normal distribution with μ = 247 and σ = 62.2. You intend to draw a random sample of size n = 16. (a) Find the probability that a single randomly selected value is greater than 295.2. (b) Find the probability that a sample of size n= 16 is randomly selected with a mean greater than 295.2. Give your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

a)

And using the normal distribution table or excel we got:

b)

And we can use the normal standard table or excel in order to find the probability and we got:

Step-by-step explanation:

For this case we know that the random variable of interest is normally distributed with the following parameters:

Part a

We want to find this probability:

And we can use the z score formula given by:

Replacing we got:

And using the normal distribution table or excel we got:

Part b

We select a random sample of size n = 16 and we try to find this probability:

And we can use the z score formula given by:

And replacing we got:

And we can use the normal standard table or excel in order to find the probability and we got:

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4