Express courier service has found that the delivery time for packages is normally distributed, with mean 13 hours and standard deviation 2 hours. (a) for a package selected at random, what is the probability that it will be delivered in 18 hours or less? (round your answer to four decimal places.) (b) what should be the guaranteed delivery time on all packages in order to be 95% sure that the package will be delivered before this time? (hint: note that 5% of the packages will be delivered at a time beyond the guaranteed time period.) (round your answer to one decimal place.)

Step-by-step explanation:

Express Courier Service has found that the delivery time for packages is normally distributed. So we use

z = (x - mean)/standard deviation

mean = 13

standard deviation = 2

x = time of delivery in hours

a) P(0 lesser than/equal to 18)

z = (18-13)/2 =5/2 = 2.5

Using the normal distribution table, the value is 0.9938

b) to be 95% sure, let the time be t

From the table, the equivalent of z that is 0.95 = 1.645

So 1.645 = (t-13)/2

t-13 = 3.29

t = 3.29+13= 16.29 hours

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

source: