Question

Loony Park has a new adult ride that holds 25 people. The maximum weight that the ride can carry is 4,226.50lb. The weight of adults has a mean of 158.86lb and a standard deviation of 18.89lb. Calculate the probability that a random group of 25 people will overload the maximum weight that the ride can carry. This is equivalent to calculating the probability that the mean weight of 25 adults would exceed 169.06lb (being 4,226.50lb divided by 25). Give your answer as a decimal to 4 decimal places.

Answer 1

Given,

= 158.86, = 18.89

Using central limit theorem,

P( < x) = P( Z < x - / ( / sqrt(n)) )

So,

P( > 169.06) = P( Z > 169.06 - 158.86 / ( 18.89 / sqrt(25) ) )

= P( Z > 2.70)

= 1 - P( Z < 2.70)

= 1 - 0.9965

= 0.0035