A survey from Teenage Research Unlimited found that 40% of teenage con

trainart1

trainart1

Answered question

2021-11-13

A survey from Teenage Research Unlimited found that 40% of teenage consumers receive their spending money from part-time jobs. If 5 teenagers are selected at random:
1. Find the probability that at least 3 of them will have part-time jobs.
2. Find the probability that no more than 4 will have part-time jobs.
3. Find the probability that less than 5 but greater than 3 will have part-time jobs.

Answer & Explanation

Ruth Phillips

Ruth Phillips

Beginner2021-11-14Added 18 answers

Step 1
Solution:
Let X be the number of teenage customers will have part-time jobs.
From the given information, probability that a teenage customer receive their spending money from part-time job is 0.40 and n=5.
Step 2
Here, teenagers are independent and probability of success is constant. Hence, X follows binomial distribution with parameters n=5 and p=0.40.
The probability mass function of binomial random variable X is
P(X=x)=(nx)px(1p)nx;x=0,1,.......,n
Step 3
1. The probability that at least 3 of them will have part-time jobs is
P(X3)=1P(X<3)
=1P(X2)
=10.6826 [Using the excel function =BINOM.DIST (2,5,0.4, TRUE)]
=0.3174
Thus, the probability that at least 3 of them will have part-time jobs is 0.3174.
Step 4
2. The probability that no more than 4 will have part-time jobs is
P(X4)=0.9898 [Using the excel function =BINOM.DIST (4,5,0.4, TRUE)]
Thus, the probability that no more than 4 will have part-time jobs is 0.9898.
Step 5
3. The probability that less than 5 but greater than 3 will have part-time jobs is
P(3<X<5)=P(X=4)
=(54)0.404(10.40)54
=0.0768
Thus, the probability that less than 5 but greater than 3 will have part-time jobs is 0.0768.

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