Suppose 6

Suppose the life span of a revolutionary light bulb is normally distributed with a mean life span of 70 thousand hours and a standard deviation of 3 thousand hours. If a light bulb is chosen at random:

a) what is the probability the life span will be within 5 thousand hours of the mean;
b) what must its lifetime be if it is to be categorized in the tallest 5%?

Correct answer:

p =  0.9522
t₂ =  76000 h

Step-by-step explanation:

$$\begin{gathered} m=70000\text{h} \\ \sigma =3000\text{h} \\ p=N(t>m+5000,m,\sigma ) \\ {z}_1=\frac{75000-m}{\sigma }=\frac{75000-70000}{3000}=\frac{5}{3}=1\frac{2}{3}\doteq 1.6667 \\ p=N(z>z_1,0,1) \\ p=0.9522 \end{gathered}$$

Use the normal distribution table.

$t_2=m+2\cdot \sigma =70000+2\cdot 3000=76000\text{h}$

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