Question

identify the type of distribution AND the probability asked for
a. a shockproof ballpen is subjected to a shock test wherein a ballpen is dropped on a floor a certain number of times. the probability that the ballpen will stop working is 0.22. let X be the number of falls in order for a ballpen to stop writing. find the probability that the pen is dropped 12 times in order for it to stop writing.

b. ilaw company delivers candles to its customers in boxes of 20. it has been discovered that 6 candles in every box won't light properly. a customer randomly selects 5 candles from a box, and demands to return the candles if at least 4 of the candles he picked will not light properly. let x denote the number of candles that won't light. what is the probability that the customer will return the candles ordered?

c. in a coffee shop, 45% of the customers prefer frapuccino. what is the probability that 6 of the bext 10 customers who will walk into the coffee shop will order frapuccino? let x be the number of customers who will choose a frapuccino drink?

Answer 1

A shockproof ballpen is subjected to a shock test wherein a ballpen is dropped on a floor a certain number of times. the probability that the ballpen will stop working is 0.22. let X be the number of falls in order for a ballpen to stop writing. find the probability that the pen is dropped 12 times in order for it to stop writing.

Prob that pen stops working = 0.22

Prob that pen will not stop working = 1-0.22=0.78

X = the number of falls in order for a ballpen to stop writing.X is a success

This means we have no success until the 12th drop.

This a Bernoulli distribution.

Prob that pen will stop working on 12th drop =

b. ILAWcompany delivers candles to its customers in boxes of 20. it has been discovered that 6 candles in every box won't light properly. a customer randomly selects 5 candles from a box and demands to return the candles if at least 4 of the candles he picked will not light properly. let x denote the number of candles that won't light. what is the probability that the customer will return the candles ordered?

Prob of faulty candles = 6/20

Prob of good candles = (1-6/20)=14/20

Customer randomly chooses 5 candles and will return the box if 4 out of 5 were faulty.

Prob that customer will return box is given by a Bernoulli trial.

He will return if 4 out of 5 were faulty.

c. in a coffee shop, 45% of the customers prefer frappuccino. what is the probability that 6 of the next 10 customers who will walk into the coffee shop will order frappuccino? let x be the number of customers who will choose a frappuccino drink?

Prob of frappuccino lover = 0.45

Prob that 6 out of 10 next customers will order frappuccino is also given by Bernoulli trail