Question

Certain tubes manufactured by a company have a mean lifetime of 800 hours and a standard deviation of 60 hours. Find the probability that a random sample of 16 tubes taken from the group will have a mean lifetime (a) between 790 and 810 hours, (b) less than 785 hours, (c) more than 820 hours, (d) between 770 and 830 hours

Answer 1

Answer:

Step-by-step explanation:

given that certain tubes manufactured by a company have a mean lifetime of 800 hours and a standard deviation of 60 hours.

Sample size n =16

Std error of sample mean = $\frac{\sigma}{\sqrt{n} } \\= 15$

x bar follows N(800, 15)

the probability that a random sample of 16 tubes taken from the group will have a mean lifetime

(a) between 790 and 810 hours,

=$P(790<x<810)\\= P(|z|<0.667)\\= 2*0.248\\= 0.496$

(b) less than 785 hours

$=P(X<785)\\=P(Z<-1)\\= 0.1584$

, (c) more than 820 hours,

$=P(X>820)\\=p(Z>1.333)\\= 0.0913$

(d) between 770 and 830 hours

=$P(|Z|<2)\\= 0.4772*2\\=0.9544$