Question

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version 2 Questions 09 - 10 Assume that the number of calories in a McDonald's Egg McMuffin is a normally distributed random variable with a mean of 290 calories and a standard deviation of 10 calories. Q09 What is the probability that a McDonald's Egg McMuffin contains between 275 and 310 calories? (a) 91.044% (b) 86.639% (e) 77.454% (d) 70.657% (e) 62.466% Answer (a) 91.044 Q10 What is the 25-percentile, i.e. bottom 25% value of the calories in a McDonald's Egg McMuffin? (a) 287.5 (b) 292.5 (e) 297.5 (d) 296.7 (e) 283.3 Answer (e) 283.3

Answer 1

Ans 1)

When 275<x<310 then finding respective z value

z1 when x>275 that is z1=(x-mean)/Population SD
z1=(275-290)/10=-1.5

z2 when x<310 that is z2=(x-mean)/Population SD
z2=(310-290)/10=2

We need to find area under Probability density curve when 275<x<310

Probability when z1=-1.5 is 0.0668
Probability when z2= 2 is 0.9772

therefore our answer must be the difference between z2 & z1 =0.9772-0.0668=0.9104

=91.04%

Option 1) is correct

Ans 2)
when Probability is 0.25 then z would be -0.68

then z=(x-mean)/SD

-0.68=(x-290)/10
-6.8=x-290

x=283.2

Hence option e) is correct