[8 points] (4) According to Hart Hotel records, 80% of all guests checking in ha
ID: 3258732 • Letter: #
Question
[8 points]
(4) According to Hart Hotel records, 80% of all guests checking in have luggage.
In a random sample of 15 guests, what is the probability that 10 or more guests will have luggage? Use the binomial table below to answer.
93.9%
10.3%
83.6%
16.4%
Data
Sample size
15
Probability of success
0.8
Statistics
Mean
12
Variance
2.4
Standard deviation
1.549193
X
P(X)
P(<=X)
P(<X)
P(>X)
P(>=X)
8
0.013819
0.018059
0.00424
0.981941
0.99576
9
0.042993
0.061051
0.018059
0.938949
0.981941
10
0.103182
0.164234
0.061051
0.835766
0.938949
11
0.187604
0.351838
0.164234
0.648162
0.835766
12
0.250139
0.601977
0.351838
0.398023
0.648162
13
0.230897
0.832874
0.601977
0.167126
0.398023
14
0.131941
0.964816
0.832874
0.035184
0.167126
15
0.035184
1
0.964816
0
0.035184
(b) If each guest is an independent event, what is the probability that the next ten guests to check in all have luggage? Round off to the nearest whole percent.
80%
16%
8%
11%
Data
Sample size
15
Probability of success
0.8
Statistics
Mean
12
Variance
2.4
Standard deviation
1.549193
X
P(X)
P(<=X)
P(<X)
P(>X)
P(>=X)
8
0.013819
0.018059
0.00424
0.981941
0.99576
9
0.042993
0.061051
0.018059
0.938949
0.981941
10
0.103182
0.164234
0.061051
0.835766
0.938949
11
0.187604
0.351838
0.164234
0.648162
0.835766
12
0.250139
0.601977
0.351838
0.398023
0.648162
13
0.230897
0.832874
0.601977
0.167126
0.398023
14
0.131941
0.964816
0.832874
0.035184
0.167126
15
0.035184
1
0.964816
0
0.035184
Explanation / Answer
P(X>=10)
n =15 ,p = 0.8
from table see X = 10 (row) and in the last column (X>=x)
=0.938949 = 0.939 = 93.9%
hence 93.9% is correct
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