Question

Statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes. Find the probability of selecting a class that runs between 51.25 and 51.5 minutes

Answer 1

Answer: The probability that a given class period runs between 51.25 and 51.5 minutes is 0.025.

The probability of selecting a class that runs between 51.25 and 51.5 minutes is 0.025.

Explanation:

Probability distribution function for uniformly distributed variable x in [a,b] in interval :
`f(x)=(1)/(b-a)`

It is given that , Statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes.

Let X be the lengths of her classes.

Then , the probability distribution function for X will be :

`f(x)=(1)/(56-46)=0.10`

Then, the probability that a given class period runs between 51.25 and 51.5 minutes will be :

`\int^(51.5)_(51.25)f(x)\ dx=0.1\int^(51.5)_(51.25)\ dx\\\\= 0.10[x]^(51.5)_(51.25)\\\\=0.10[51.5-51.25]=0.025`

Hence, probability that a given class period runs between 51.25 and 51.5 minutes is 0.025.

It is same for the probability of selecting a class that runs between 51.25 and 51.5 minutes.