Question

A bridge across a deep jorge has a capacity of 5184 pound. If the weights of tourists have a mean of 160 pounds and a standard deviation of 38 pounds, find the probability that a group of 32 not-overly-bright tourists who attempts to cross the gorge simultaneously will plummet to a grisly death. (Hint: the groups weight will exceed 5184 pounds if the mean weight in the group is over 162 pounds)

Answer 1

Solution :

Given that ,

mean = = 160

standard deviation = = 38

n = 32

=   = 160

= / n = 38 / 32 = 6.72

P( > 162 ) = 1 - P( < 162 )

= 1 - P[( - ) / < (162 -160) / 6.72]

= 1 - P(z < 0.30 )

Using z table,    

= 1 - 0.6179

= 0.3821