5. Binomial Distribution & Discrete Random Variables

Which of the following is a binomial experiment?

A sales representative makes 6 cold calls in a day. The probability of successfully making a sale on any given call is 40%. Find the probability of making a sale on all 6 calls.

National surveys indicate that 36% of people have been in a car accident in the last 5 years. If you randomly sample 10 people, how likely is that exactly 4 have had an accident in the last 5 years?

Based on historical weather data in a certain city, about 62% of the days are cloudy. Find the mean, standard deviation, and variance for the number of cloudy days in a 30-day month.

A gardener plants 8 seeds, and each has a 65% probability of germinating successfully. Find the probability that less than 4 seeds germinate successfully.

A biologist is monitoring a large bird sanctuary where a particular bird species is known to have a 70% success rate for each nesting attempt (at least one chick fledges from the nest). This season, she observes 500 independent nesting attempts across the sanctuary.

(A) What is the probability that exactly 450 nesting attempts are successful?

A biologist is monitoring a large bird sanctuary where a particular bird species is known to have a 70% success rate for each nesting attempt (at least one chick fledges from the nest). This season, she observes 500 independent nesting attempts across the sanctuary.

(B) What is the probability that less than 330 attempts are successful?

A biologist is monitoring a large bird sanctuary where a particular bird species is known to have a 70% success rate for each nesting attempt (at least one chick fledges from the nest). This season, she observes 500 independent nesting attempts across the sanctuary.

(C) What is the probability that at least 330 nesting attempts are successful?

A biologist is monitoring a large bird sanctuary where a particular bird species is known to have a 70% success rate for each nesting attempt (at least one chick fledges from the nest). This season, she observes 500 independent nesting attempts across the sanctuary.

(D) What is the probability that 330 – 370 nesting attempts are successful?

A retail company sends out promotional emails and finds that approximately 1.5% of emails sent through their system are flagged as spam by users. On a given day, 20,000 emails are sent through the system.

(B) If more than 350 emails are flagged as spam, should this be investigated? 

A retail company sends out promotional emails and finds that approximately 1.5% of emails sent through their system are flagged as spam by users. On a given day, 20,000 emails are sent through the system.

(A) What is the probability that more than 350 emails are flagged as spam?