221k views
0 votes
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

User Abuzze
by
7.9k points

1 Answer

1 vote

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.

User Wahwahwah
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories