Daily water intake (including water used in drinks such as coffee, tea and juice) for Canadian adults follows a normal distribution with mean 1.86 litres and standard deviation 0.29 litres.
(a) Can you calculate the probability that the mean daily water intake for a random sample of two Canadian adults is less than 1.65 litres? If you can, enter the probability in the answer box. If you can't, type the word No.
(b) What is the probability that the mean daily water intake for a random sample of 31 Canadian adults is greater than 1.8 litres?
(c) What is the probability that the total daily water intake for a random sample of 41 Canadian adults is between 72.43 and 77.73 litres?
(d) Using the 68-95-99.7 Rule, approximately 95% of samples of 24 Canadian adults will have mean daily water intakes between and .
(e) If we take a random sample of 15 Canadian adults, there is an 11% chance that their mean daily water intake will be greater than
3 answers
P(X<1.65)=P[Z<(1.65-1.86)/(0.29/√2)
Your answer should be P(Z<-0.98), You would then look at the Standard Normal probabilities table, which should give you, 0.1660.
b) would be the same formula but you would use (1.8-1.86) and your squareroot would be √36 instead. Then again you would use the Standard Normal probabilities table, once you get your answer from there you have to do 1-n
n=the answer from Standard Normal probabilities table
c)Step 1: P(72.43/41<X< 77.73/41) P=(1.7666 <X< 1.8959)
Step 2: P[(1.7666-1.86)/(0.29/√41)] and (1.8959-1.86)/(0.29/√41)
Step 3:Once you get your answers again use the Standard Normal probabilities table.
Step 4: Bigger number minus smaller number. That should give you your answer.
d) For the first part
μ= 1.86
σ=0.29
n= 24
Use this formula; μ-2(σ/√n)
For the second part use: μ+2(σ/√n)
(e) Not a 110% about this one sorry. But the formula should be similar as previous, where z=1.23...I think.
x= μ+z(σ/√n)
7 answers