The average temperature of a particular tropical island is normally distributed with a mean of 74 degrees and a variance of 9 degrees
(a) If a random sample of 16 days has been taken, what is the probability that at least 12 of them will have temperatures higher than 70 degrees?
(b) If a random sample of 16 days has been taken, what is the probability that the sample standard deviation is within 1 unit from the population standard deviation?
for part (a) i get 0.99.
part b is not something with which i feel very acquainted. could anyone tell me the approach?
I feel the problem is asking
$$ P(-\sigma < s < \sigma ) $$ And I can use the fact that
$$ \frac{(n-1)s^2}{\sigma^2} \ follows \ X^2(n-1) $$
But I am not sure how to proceed, because I do not know what is s