Answer: C) 0.8664.
Explanation:
Given, The tread life of tires mounted on light-duty trucks follows the normal probability distribution with
.
Let
be the sample mean tire life of any 4 tires.
Now , the probability that the mean tire life of these four tires is between 57,000 and 63,000 miles will be :-
![P(57000<\overline{x}<63000)=P((57000-60000)/((4000)/(√(4)))<\frac{\overline{x}-\mu}{(\sigma)/(√(n))}<(63000-60000)/((4000)/(√(4))))\\\\=P(-1.5<z<1.5)\ \ \ [\because\ z=\frac{\overline{x}-\mu}{(\sigma)/(√(n))} ]\\\\= P(z<1.5)-P(z<-1.5)=P(z<1.5)-(1-P(z<1.5))\\\\=0.9332-(1-0.9332)\ \ [\text{By z-table}]\\\\=0.8664](https://img.qammunity.org/2021/formulas/mathematics/high-school/47bcrurt5qg0y5lur8doy2qvkpypaodpel.png)
For Very likely , the probability should lie between 0.95 and 1.
Hence, the correct answer is C) 0.8664.