A variable is normally distributed with mean 10 and standard deviation 2. a. Det

Question

A variable is normally distributed with mean 10 and standard deviation 2. a. Determine the quartiles of the variable. b. Obtain and interpret the 85th percentile. c. Find the value that 65% of all possible values of the variable exceed. d. Find the two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025. Interpret the answer. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. Q_1 = Q_2 = Q_3 =

Explanation / Answer

a)

q1 corresponds to 25% below this value
z=-0.67448975
now we need to get the variable x = -0.67448975*2+10 = 8.651021
the same logic for q3
z=0.67448975
now we need to get the variable x = 0.67448975*2+10 = 11.348980
Answer: 8.651 and 11.349

b)

85th percentile means 85% of the area unde the curve
is to the left of that number:
get the z first using normsinv function in excel
z = 1.036433389
hence x = 1.036433389 * 2+10 = 12.072866778
Answer: 12.07

c)

it is 65th percentile and use the same logic
z = 0.385320466
hence
x=0.385320466*2+10 =10.770640932
Answer: 10.77

d)

this is z=-1.96 ans z=1.96
and hence x = -1.96*2+10=6.08
and x= 1.96*2+10=13.92
Answer: 6.08 and 13.92

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