Question

The length of life of an instrument produced by a machine has a normal distribution with a mean of $12$ months and standard deviation of $2$ months. Find the probability that an instrument produced by this machine will last less than $7$ months.

• A. $0.2316$
• B. $0.0062$
• C. $0.0072$
• D. $0.2136$

Answer 1

The correct option is B $0.0062$

Life of intsrument follows normal distribution.

Given mean i.e. $\mu$ $=12$months

Given standard deviation i.e. $\sigma$ $=2$ months

The normal random variable of a standard normal distribution is called a standard score or a z-score. Every normal random variable X can be transformed into a z score via the following equation:

$z=(X-\mu )/\sigma$

where $X$ is a normal random variable, $\mu$ is the mean of $X$, and $\sigma$ is the standard deviation of $X$.

For $X=22$

$Z=(7-12)/2=-2.5$

$P(X<7)=P(Z<-2.5)$

$=0.0062$