Please show all steps . Thank you In order to get into ABC college you need to s

Question

Please show all steps . Thank you In order to get into ABC college you need to score in the top 8% of its placement test. The test results are normally distributed with a mean of 800 pts and a standard deviation of 50 pts. VY hat is the minimum scored needed in the test in order to get into ABC College? The amount of caffeine in energy drinks is approximately normally distributed with mean of 80 milligrams and a standard deviation of 7 milligrams. (a) What is the probability that a randomly chosen drink will contain less than 66 milligrams.

Explanation / Answer

Question 4

Mean score for the test = 800 marks

standard deviation for the test = 50 marks

Lets say x is the cuoff score above that students get admission in ABC college.

so Pr( Score > x ; 800 ; 50) = 0.08

Pr( Score < x ; 800; 50) = 1- 0.08 = 0.92

so we will look into Z - table, we will see the value of probability value for the relative value of Z .

so Here from Z - table; Z = 1.405

(x - 800)/ 50 = 1.405

x = 800 + 50 * 1.405 = 870.25 marks

soone shouldget above 870.25 marks to get admission into XYZ college.

Question 5

MEan amount of caffeine = 80 mg

Standard deviation of caffeine = 7 mg

(a) Pr (Caffeiene content < 66 mg ; 80 ; 7) = ?

We will find the Z - value

here, Z = (66 - 80)/ 7 = -2

so for Z = -2,  Pr (Caffeiene content < 66 mg ; 80 ; 7) = 0.0228

that means, there are 2.28% chance that a randomly chosen drink will contain less than 66 mg.

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