Question

Assume the random variable X is normally​ distributed, with mean muμequals=4141 and standard deviation sigmaσequals=88. Find the 6 th6th percentile. The 6 th6th percentile is nothingm.

Answer 1

Solution

given: p= 41, o = 8

formula : Z = *-*

6th percentile = P(Z <?) = 0.06

From Z-table, Lookup for Z-value corresponding to area 0.06 to the left of the normal curve or use excel function " NORM.S.INV(0.06) " to the find the Z-value.

= P(Z < -1.55) = 0.06

3 :? _P_6 1 _6 _1 _2 _3

Inverse Normal distribution

—155 = X-41

X = 41 +(-1.55*8)

X = 41 – 12.40

X = 28,60

The 6th percentile is 28.60