Question

A popular resort hotel has 400 rooms and is usually fully booked. About 5% of the time a reservation is canceled before the 6:00 p.m. deadline with no penalty. What is the probability that at least 376 rooms will be occupied? Use the binomial distribution to find the exact value. The probability is (Round to four decimal places as needed.)

Answer 1

Hello

YOUR REQUIRED ANSWER IS 0.8490

Given that:

p	5.00%
n	400

Using

$P(X=r)=\binom{n}{r}p^r(1-p)^{n-r}$

We get :

x	P(x)
0	0.0000
1	0.0000
2	0.0000
3	0.0000
4	0.0000
5	0.0000
6	0.0001
7	0.0004
8	0.0011
9	0.0025
10	0.0052
11	0.0096
12	0.0165
13	0.0259
14	0.0376
15	0.0509
16	0.0645
17	0.0767
18	0.0859
19	0.0909
20	0.0911
21	0.0868
22	0.0787
23	0.0681
24	0.0563

Hence,

P(X upto 24) = 0.8490 = 84.9%

Thanks!

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