3 sigma

Students' performance scores in a statistic test have a mean of 70 and a standard deviation of 4.0. The scores obtained can be modeled by a normal distribution. Find the probability that the score of a randomly selected student is

i. more than 80 marks
ii. less than 65 marks

Find also the number of students who scored above 80 marks if a total of 1200 students sat for the test.

Correct answer:

a =  0.0062
b =  0.1056
c =  7

Step-by-step explanation:

μ=70 σ=4.0  z1=σ80μ=48070=25=221=2.5  80 = μ+2.5 σ  a=0.0062

Use the normal distribution table.
z2=σ65μ=46570=45=141=1.25 65 = μ1.25 σ  b=0.1056

Use the normal distribution table.
n=1200 c=[a n]=[0.0062 1200]=7

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