2 Probability HELP please!

[newbiestats]

Two more questions on probability if someone could help me out please and thankyou

The article “Reliability of Domestic-waste Bio?lm Reactors” suggests that substrate concentration (mg/cm3 )
of in?uent to a reactor is normally distributed with µ = 0.30 and ? = 0.06.

(a) What is the probability that the concentration exceeds 0.25?
(b) What is the probability that the concentration is at most 0.10?

A cola-dispensing machine is set to dispense on average 250 mL of cola per cup. The standard deviation
is 4 mL. The distribution of the amounts dispensed follows a normal distribution.

(a) What is the probability that the machine will dispense between 253 mL and 258 mL of cola?
(b) What is the probability that the machine will dispense 260 mL of cola or more?
(c) What is the probability that the machine will dispense between 245 mL and 255 mL of cola?

 

[tutor_joel]

(corrected) I made a couple of mistakes on the first version of this

you need the formula Z = (x - u)/s where x = 0.25, u = 0.3 and s= 0.06. (This z score will help you find the probability,which is used in the hypothesis test Ho > 0.25 from a standard normal distribution. Area under the curve is equal to one. The bell shaped curve)

z = -0.8333

Probability(x > 0.25) should be a high number since the mean is 0.3.
z = -0.8333

now you need a normal distribution table and you have to look up the area with z = -0.8333 (with a 95% confidence interval is standard). You would get 0.8023. Now this is the area from the center of the bell shaped curve. (depending on the table you're using, some only give an area from the center of the curve)


P(x > 0.25) = 0.8023 or 80%

or, the answer could just be 0.8333 if there is no confidence interval.

now, "at most" means that number never exceeds a given condition.

So, x < 0.1, this should be a very low number. You do not add the other half of the curve to this one. Since it's the area from the center, you need to subtract this number from 1 in order to fit the condition x < 0.1

Let me know if this makes any sense. Do you have the table?