Question

A waiter believes that tips are normally distributed with a mean of $9.60 and a standard deviation of $2.40.

A. What percentage of the tips are above %8.50?

B.What percentage of the tips are below $8.00?

C. What percentage of tips are between $9.00 and $10.00?

D. Find the minimum tip in the top 3.25% of the normal distribution.

E. Find the maximum tip in bottom 5% of the normal distribution.

Answer 1

Solution :

A waiter believes that tips (say X) are normally distributed with a mean of $9.60 and a standard deviation of $2.40.

(a). The  probability of the tips are above $ 8.50 is given by;

P( X > 8.50 ).

The Z score for 8.5 = (8.5 - 9.6) / 2.4 = - 0.4583.

So P ( X > 8.5 ) = P (Z > - 0.4583 ) = 1 - P ( Z < - 0.4586 ) = 1 - 0.3234 = 0.6366.

And hence the 63.66% percentage of tips above $8.50.

(b). The  probability of the tips are below $ 8 is given by;

P( X < 8 ).

The Z score for 8 = (8 - 9.6) / 2.4 = - 0.6667

So P ( X < 8) = P (Z > - 0.6667 ) = = 0.2525.

And hence the 25.25% percentage of tips below $8.