Question

7.)     The average cholesterol content of Mighty Taco’s Super Mighty Burrito is 95 mg with a standard deviation of 7.2. Assume the variable is normally distributed.

(a)    If a single Super Mighty Burrito is purchased, find the probability it will have less than 100 milligrams of cholesterol.

(b)    If you purchase a Super Mighty 4 pack, which consists of 4 Might taco Super Mighty Burritos, find the probability that the mean of the sample will be larger than 100 milligrams of cholesterol.

Answer 1

Solution :

Given that ,

mean = = 95

standard deviation = = 7.2

a) P(x < 100) = P[(x - ) / < (100 - 95) / 7.2 ]

= P(z < 0.69 )

Using z table,

= 0.7549

b) n = 4

=   = 95

= / n = 7.2 / 4 = 3.6

P( > 100) = 1 - P( < 100)

= 1 - P[( - ) / < (100 - 95) / 3.6 ]

= 1 - P(z < 1.39 )

Using z table,    

= 1 - 0.9177

= 0.0823