The Life Span of a Car Battery is Normally Distributed with a Mean of 44 Months and Standard Deviation 5 Month?

A) a car battery is selected at random. ind the probability that the life span of the battery is less than 36 months.

B) a car battery is selected at random. find the probability that the life span of the battery is between 42 and 60 months.

C) what is the shortest life expectancy battery a car battery can have and still be in the top 5% of the life expectancies?

Suggestion:

A. ANSWER: The probability of the sample less than 36 = 5%.

Why???

NORMAL DISTRIBUTION, STANDARDIZED VARIABLE z, PROBABILITY "LOOK-UP"
STANDARDIZED VARIABLE: z = (x – µ)/(σ/√(n))
= (36 – 44)/(5/√(1)) = -1.6

SAMPLE MEAN: x = 36
POPULATION MEAN: µ = 44
POPULATION STANDARD DEVIATION: σ = 5
SAMPLE SIZE: n = 1

SIGNIFICANT DIGITS = 2

The Table for Standard Normal Distribution is organized as a cummulative 'area' from the LEFT corresponding to the STANDARDIZED VARIABLE z. For STANDARDIZED VARIABLE z = -1.6 the corresponding area = 0.05.

B. ANSWER: 66% between 42 and 60 months.

C. ANSWER: 52.2months
Why??
95% "Look-up" from STANDARDIZED NORMAL TABLE, z = 1.64
MONTHS = 44 + 1.64 * 5