Question

On the distant planet Cowabunga , the weights of cows have a normal distribution with a mean of 347 pounds and a standard deviation of 37 pounds. The cow transport truck holds 13 cows and can hold a maximum weight of 4654. If 13 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 4654? (This is the same as asking what is the probability that their mean weight is over 358.)

Answer 1

Let random variable x be weights of cows which is normally distributed with

mean = = 347 and

standard deviation = = 37

n = sample size = 13

Here we have to find

According to Central limit theorem, if random variable X has normal distribution then sampling distribution of sample mean is approximately normally distributed with mean = and standard deviation

=

Mean of

Standard deviation of              (Round to 3 decimal)

              Where SD is standard deviation

                                           Where z is standard normal variable

                         = P(z > 1.07)                         (Round to 2 decimal)

                         = 1 - P(z < 1.07)

                        = 1 - 0.8577               (From statistical table of z values)

                       = 0.1423

The probability that the mean weight is over 358 is 0.1423