Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 798 hours and a standard deviation of 80 hours. Find the probability that a random samples of 39 bulbs will have an average life of less than 814 hours

Answer 1

$P(X<814)=P(Z< \frac{814-798}{ \frac{80}{ \sqrt{39} }})$

$P(X<814)=P(Z<1.25)$

From using normal distribution table, probability is:

$P(X<814)=0.8944$

There is 89.44% probability that a random samples of 39 bulbs will have an average life of less than 814 hours.