Usually about 65% of the patrons of a restaurant order burgers. A restaurateur anticipates serving about 160 people on Friday. LetXbe the numbers of burgers ordered on Friday. ThenXis binomially distributed with parametersn= 160 andp= 0.65.

What is the expected number of burgers (_X) ordered on Friday? [Answer up to 2 digits after decimal]

Find the standard deviation ofX(_X)? [Answer up to 3 digits after decimal]

If the restaurant ordered meats to prepare bout 111 burgers for Friday evening. Use normal approximation of binomial distribution to find the probability that on Friday evening some orders for burgers from the patron cannot be met. [Answer up to 4 digits after decimal]

How many burgers the restaurant should prepare beforehand so that the chance that an order of burger cannot be fulfilled is at most 0.02? i.e.

Findasuch thatP(X>a) = 0.02 using normal approximation of binomial distribution.