Question

1). Suppose the weight of a cow is N ( 20000, 400 ). You buy a baby cow. Find the probability that your baby cow will eventually weigh 20100 pounds or more.

2) How much would you cow have to weigh in order to be bigger than 95% or all cows?

3) There are 1000 marbles in a box. Their diameters are D = N ( 1, .25 ). You choose 100 marbles from the box and put them back. Many other people do the same. ( The person with the largest average diameter wins a car. ). Find the mean and standard deviation for their averages.

4) There are 9 dogs of a certain kind in your neighborhood. The weight of this kind of dog is normally distributed with the mean = 100 pounds and standard deviation = 10 pounds. D = N ( 100, 10 ). What is the mean and standard deviation of the distribution of the average weights of 9 such dogs?

Answer 1

1. Let X be a random variable denoting the weights of cows. We are given that . We are to determine the probability that X is greater than or equal to 20100 pounds i.e.

Converting this probability into Standard normal variate, we get:

  

From normal tables , we get,

The required probability is 0.4013

2. In the above question, we have to calculate P(X>x)=0.95

  Converting this probability into Standard normal variate, we get:

  

From normal tables , we get,

or,

The required weight a cow should have is 20658 pounds.

Please post other questions separately.