Question

5. You are the extremely brilliant business statistician hired to analyze the data at Elliot's World o' Tacos. Elliot wants to make sure that the high school kids he hired are putting the right amount of cheese (2oz) on the tacos. Too much cheese and he will lose money! Too little cheese and people complain. The tacos that should have 2 oz of cheese actually vary in amount with a standard deviation of 0.15 ounces. Assume the cheesiness of the tacos is normally distributed a. What percentage of all tacos made contains more than 2.22 ounces of cheese? b. What percentage of all tacos made contains less than 1.50 ounces? c. What percentage of tacos made contains between 1.46 to 2.38 ounces? d. Ninety-five percent of the tacos will contain at least how many ounces of cheesy goodness? e. What percentage of the tacos contains between 1.41 and 1.78 ounces?

Answer 1

c) For n= 2= x-M 1.46 1:46-2 0.15 Z = -3.6 for n=2.38 2= n-M 2.38-2 0:15 2=-3.6 2-2.53 . Using a table 2= 2153 2- 2.53 z table, area under the curve to the left of 2= -3.6 is 0.00016 and area under the curve to the left of is 0.9943 :. Area of shaded region - 0.9943 -0.00016 = 0.99414 Thesefore the percentage of facas made that contains between 1.46 and 2.38 99.41 / ounces is d) 95% 04 atos must contain at least a perticular value or amount of cheese. That means sile of tacos contain amount of cheese below that perticular value. i. Using a table, value of a corresponding to area 0,05 is Z= -1.64 2017 Now , 2=n-M SM Z=-1,64 N= 24 tu

. (-1:64) (0.15)&2 1.754 Therefore 95% of the tacos will contain at least 1.954 ounces of cheesy goodness' e) For n=1.41 2=n-M = 1.41-2 0.15 Z: - 3.93 for n=1.78 2=n-u 1.78-2 0:15 - 2--3.93 2-1.47 2= -1,47 Using a table area area to the left of 2 = -3.93 is 0.00004 and area to the left of z=-1:47 is o oror8 i Area of shaded region = 0.07078 - 0.00004 = 0.07074 :: The percentage of the tacos that containe between 1.41 and 1.78 ounces cheese is 7.07 %