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

trainart1 2021-11-13 Answered
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.

Want to know more about Probability?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Ruth Phillips
Answered 2021-11-14 Author has 8155 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 \(\displaystyle{n}={5}\).
Step 2
Here, teenagers are independent and probability of success is constant. Hence, X follows binomial distribution with parameters \(\displaystyle{n}={5}\ {\quad\text{and}\quad}\ {p}={0.40}\).
The probability mass function of binomial random variable X is
\[P(X=x)=\left(\begin{array}{c}n\\ x\end{array}\right) p^{x}(1-p)^{n-x}; x=0,1,.......,n\]
Step 3
1. The probability that at least 3 of them will have part-time jobs is
\(\displaystyle{P}{\left({X}\geq{3}\right)}={1}-{P}{\left({X}{<}{3}\right)}\)
\(\displaystyle={1}-{P}{\left({X}\leq{2}\right)}\)
\(\displaystyle={1}-{0.6826}\) [Using the excel function =BINOM.DIST (2,5,0.4, TRUE)]
\(\displaystyle={0.3174}\)
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
\(\displaystyle{P}{\left({X}\leq{4}\right)}={0.9898}\) [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
\(\displaystyle{P}{\left({3}{<}{X}{<}{5}\right)}={P}{\left({X}={4}\right)}\)
\[=\left(\begin{array}{c}5\\ 4\end{array}\right) 0.40^{4} (1-0.40)^{5-4}\]
\(\displaystyle={0.0768}\)
Thus, the probability that less than 5 but greater than 3 will have part-time jobs is 0.0768.

Not exactly what you’re looking for?
Ask My Question
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-05-30
Justine works for an organization committed to raising money for Alzheimer’s research. From past experience, the organization knows that about 20% of all potential donors will agree to give something if contacted by phone. They also know that of all people donating, about 5% will give $100 or more. On average, how many potential donors will she have to contact until she gets her first $100 donor?
asked 2021-10-20
Based on a poll, 40% of adults believe in reincarnation. Assume that 6 adults are randomly selected, and find the indicated probability. What is the probability that at least 5 of the selected adults believe in reincarnation? The probability that at least 5 of the selected adults believe in reincarnation is |_| (Round to three decimal places as needed.)
asked 2021-09-20
a simple binary communication channel carries messages by using only two signals, say 0 and 1. We assume that, for a given binary channel, 40% of the time a | is transmitted. the probability that a transmitted 0 is correctly received is 0.90 and the probability that a transmitted | is correctly received is 0.95. the probability of a 1 being received
asked 2021-09-21
An oil company is bidding for the rights to drill a well in field A and awell in field B. The probability it will drill a well in field A is 40%. Ifit does, the probability the well will be successful is 45%, The probability it will drill a well in field B is 30% If'it does, the probability the well will be successful is 55%, Calculate ‘each of the following probabilities: Probability of both a successful well in field A and a successful well in field B,
asked 2021-09-06
An oil company is bidding for the rights to drill a well in field A and awell in field B. The probability it will drill a well in field A is 40%. Ifit does, the probability the well will be successful is 45%, The probability it will drill a well in field B is 30% If'it does, the probability the well will be successful is 55%, Calculate ‘each of the following probabilities: Probability of a successful well in field A,
asked 2021-09-06
Rivers Casino did an audit of all of their blackjack tables and found that the amount of money collected per night by a certain table has a mean of $6,000, a standard deviation of $200, and is approximately normally distributed.
What is the probability that a table will collect less than $6000 tomorrow night?
asked 2021-08-17
A company with a fleet of 150 cars found that the emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that more than 20% of the fleet might be out of compliance? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question
...