Answer :
Answer:
The lifetime of bulb should be 1623.074 hours or more to lie in the top 10%.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 1550 hours
Standard Deviation, σ = 57 hours
We are given that the distribution of lifetimes of the light bulbs is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.10
[tex]P( X > x) = P( z > \displaystyle\frac{x - 1550}{57})=0.10[/tex]
[tex]= 1 -P( z < \displaystyle\frac{x - 1550}{57})=0.10[/tex]
[tex]P( z < \displaystyle\frac{x - 1550}{57})=0.9[/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 1550}{57} = 1.282\\\\x = 1623.074[/tex]
Thus, the lifetime of bulb should be 1623.074 hours or more to lie in the top 10%.