Answer:
The probability that a random sample of n = 5 specimens will have a sample values that falls in the interval from 2499 psi to 2510 psi = P(2499 < x < 2510) = 0.192
Step-by-step explanation:
For the population,
μ = 2500 psi and σ = 50 psi
But for a sample of n = 5
μₓ = μ = 2500 psi
σₓ = σ/√n = (50/√5)
σₓ = 22.36 psi
So, probability that the value for the sample falls between 2499 psi to 2510 psi
P(2499 < x < 2510)
We normalize/standardize these values firstly,
The standardized score for any value is the value minus the mean then divided by the standard deviation.
For 2499 psi
z = (x - μ)/σ = (2499 - 2500)/22.36 = - 0.045
For 2510 psi
z = (x - μ)/σ = (2510 - 2500)/22.36 = 0.45
To determine the probability the value for the sample falls between 2499 psi to 2510 psi
P(2499 < x < 2510) = P(-0.045 < z < 0.45)
We'll use data from the normal probability table for these probabilities
P(2499 < x < 2510) = P(-0.045 < z < 0.45) = P(z < 0.45) - P(z < -0.045) = 0.674 - 0.482 = 0.192
You made a mistake with the probability 
, which should be 
in the last expression, so to be clear I will state the expression again.
So we want to solve the following:
Conditioned on this event, show that the probability that her paper is in drawer 
, is given by:
(1) 
and
(2) 
so we can say:
is the event that you search drawer 
and find nothing,
is the event that you search drawer and find the paper,
is the event that the paper is in drawer 
this gives us:
Solution to Part (1):
if 
, then 
,
this means that
as needed so part one is solved.
Solution to Part(2):
so we have now that if = , we get that:
remember that:
this implies that:
so we just need to combine the above relations to get:
as needed so part two is solved.
It will take her 54 days to take 10 more tests
That dont een make no sense tho
