The amount of time it takes Michelle to make a grilled cheese sandwich is continuous and uniformly distributed between 3 minutes and 11 minutes. What is the probability that it takes Michelle between 4 and 5 minutes given that it takes less than 6 minutes for her to make a grilled cheese sandwich?

the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)

Step-by-step explanation:

since the random variable X= time taken to make a grilled cheese sandwich is uniformly distributed, then the probability is governed by

P(a<X<b)= proportion of the time considered / total time range = (a-b)/(c-d) , where c is the maximum time and d is the minimum one

then

P(4<X<5) = (5-4)/(11-3) = 1/8 = 0.125

since we already know that takes less than 6 minutes , then

P(X<6)= P(3<X<6) = (6-3)/(11-3) = 3/8 = 0.375

then using the theorem of Bayes

P( 4<X<5 | X<6 ) = P ( 4<X<5 ∩ X<6 ) / P(X<6) = P(4<X<5)/P(3<X<6) = 0.125 /0.375 = 1/3 (33.33%)

therefore given that we already know that will take Michelle less than 6 minutes , the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)

question

what is the value of the third quartile of the data set represented by this box plot? a. 19 b. 21 c. 26 d. 29

answer

c

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b