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:

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

idk

step-by-step explanation: