In: Statistics and Probability
In your rental shop, you know that on the busiest day you can expect 150 rentals. You also know that, historically, 60% of your customers rent skis and 40% rent snowboards.
a) If you decide that you only need to have 65 snowboards in stock, what is the probability that you will run out of snowboard rentals on any specific day?
[ Choose ] 0.2259 0.1794 0.5310 0.0575 0.0664 0.5966 0.0409 0.0000
b) What if you increase your supply to 70 showboards. Now, what is the probability that you will run out?
[ Choose ] 0.2259 0.1794 0.5310 0.0575 0.0664 0.5966 0.0409 0.0000
c) What is the probability that you will rent at most 90 skis on any given day?
[ Choose ] 0.2259 0.1794 0.5310 0.0575 0.0664 0.5966 0.0409 0.0000
d) What is the probability that you will rent exactly 90 skis on any given day
n = 150 …total number of rentals
on a day
Let X be the number of snowboards rented on a
day
p = probability of renting a snowboard
= 0.4
(40%)
Then X ~ Binomial(n = 150, p = 0.4)
a) To find P(we run out of snowboards if we stock 65
snowboards)
that is to find P(X > 65)
P(X > 65) = 1 - P(X ≤ 65)
We use Excel function BINOM.DIST to find the
probability
P(X > 65) = 1 - BINOM.DIST(65, 150, 0.4,
TRUE)
= 1 - 0.8206
= 0.1794
Answer
0.1794
b) To find P(we run out of snowboards if we stock 70
snowboards)
that is to find P(X > 70)
P(X > 70) = 1 - P(X ≤ 70)
We use Excel function BINOM.DIST to find the
probability
P(X > 70) = 1 - BINOM.DIST(70, 150, 0.4,
TRUE)
= 1 - 0.9591
= 0.0409
Answer
0.0409
c) Let Y be the number of skis rented on a given
day
p' = probability of renting a ski = 0.6
-60%
Then Y ~ Binomial(n = 150, p = 0.6)
To find P(we rent atmost 90 skis on a given
day)
that is to find P(Y ≤ 90)
We use Excel function BINOM.DIST to find the
probability
P(Y ≤ 90) = BINOM.DIST(90, 150, 0.6, TRUE)
= 0.5310
Answer
0.5310
d) To find P(we rent exactly 90 skis on a given
day)
that is to find P(Y = 90)
We use Excel function BINOM.DIST to find the
probability
P(Y = 90) = BINOM.DIST(90, 150, 0.6,
FALSE)
(For discrete probability,
last parameter is FALSE)
= 0.0664
Answer
0.0664