Question

 A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell to every one and no fewer. through observation, the baker has established a probability distrubution. 

x	P(x)
1	0.10
2	0.45
3	0.30
4	0.15

A- Define the random variable X

B- what is the probability the baker will sell more than one batch? P(x > 1)

C- On average, how many batches should the baker make? (find Mean) 

D- Find the standard deviation

*Show all work / formulas

 

 

Answer 1

A) X is the number of batches.

B) P(X>1)=1-0.1=0.9=0.45+0.30+0.15

C) The mean is found by working out X*P(X) for each row and finding the sum:

1*0.1+2*0.45+3*0.30+4*0.15=2.5 so the mean is 2.5 batches.

D) The variance is the sum of X²P(X) less the mean squared:

1*0.1+4*0.45+9*0.30+16*0.15-2.5²=7-6.25=0.75. So the SD=√0.75=0.866.