A viral infection is spread by contact with an infected person. Suppose that an
ID: 3155378 • Letter: A
Question
A viral infection is spread by contact with an infected person. Suppose that an infected person has contact with 15 healthy people, let X denote the number of people (out of those 15) who are infected By "infected" we mean that the person develop symptoms of the infection. Circle the name for the Probability distribution of the random variable X. Chi-Squared Normal Binomial Gaussian Construct a table for the probability distribution in [a], if the infection rate is 25%. What values of X are consistent with an infection rate of 25% or lower. Explain. What values of X suggest that the infection rate is higher than 25%? Explain.Explanation / Answer
Answer part a
Binomial
Answer part b
The probability distribution table is given as below:
Here, n = 15 and p = 0.25 or 25%
X
P(X)
0
0.01336346
1
0.06681731
2
0.15590705
3
0.22519907
4
0.22519907
5
0.16514598
6
0.09174777
7
0.03932047
8
0.01310682
9
0.00339807
10
0.00067961
11
0.00010297
12
0.00001144
13
0.00000088
14
0.00000004
15
0.00000000
Total
1.00000000
Answer part c
The values of x called to be consistent for which the probability is at least 0.05. The consistent and inconsistent values of X are summarised in the following table:
X
P(X)
Consistency
0
0.01336346
Inconsistent
1
0.06681731
Consistent
2
0.15590705
Consistent
3
0.22519907
Consistent
4
0.22519907
Consistent
5
0.16514598
Consistent
6
0.09174777
Consistent
7
0.03932047
Inconsistent
8
0.01310682
Inconsistent
9
0.00339807
Inconsistent
10
0.00067961
Inconsistent
11
0.00010297
Inconsistent
12
0.00001144
Inconsistent
13
0.00000088
Inconsistent
14
0.00000004
Inconsistent
15
0.00000000
Inconsistent
Total
1.00000000
Answer part d
There are no any values of x which suggest more than 25% infection rate.
X
P(X)
0
0.01336346
1
0.06681731
2
0.15590705
3
0.22519907
4
0.22519907
5
0.16514598
6
0.09174777
7
0.03932047
8
0.01310682
9
0.00339807
10
0.00067961
11
0.00010297
12
0.00001144
13
0.00000088
14
0.00000004
15
0.00000000
Total
1.00000000
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