Question

X is a normally distributed random variable with a mean of 7.0 and a standard deviation of 3.00. Find the value x such that P(X < x) is equal to 0.86. (Note: the diagram is not necessarily to scale.)

		10.24
		11.63
		7.00
		8.14

Answer 1

X ~ N ( µ = 7 , σ = 3 )
P ( X < x ) = 86% = 0.86
To find the value of x
Looking for the probability 0.86 in standard normal table to calculate critical value Z = 1.08
Z = ( X - µ ) / σ
1.08 = ( X - 7 ) / 3
X = 10.24