(a) What is the probability that a randomly selected time interval between eruptions is longer than 75 minutes?
The probability that a randomly selected time interval is longer than 75 minutes is approximately. (Round to four decimal places as needed.)
(b) What is the probability that a random sample of 11 time intervals between eruptions has a mean longer than 75 minutes?
The probability that the mean of a random sample of 11 time intervals is more than 75 minutes is approximately. (Round to four decimal places as needed.)
Answer:
Given Data :
The population mean $(μ)=63$
The population standard deviation $(\sigma)=25$
(A) The probability that a randomly selected time interval is longer than 75 minutes:
$P(x > 75) = P\left(\frac{x – \mu}{\sigma} > \frac{75 – 63}{25}\right) = P(z > 0.48) = 0.3156$
(B) The probability that the mean of random sample 11 time intervals is more than 75 minutes:
$P(\overline{x} > 75) = P\left(\frac{\overline{x} – \mu}{\frac{\sigma}{\sqrt{n}}} > \frac{75 – 63}{\frac{25}{\sqrt{11}}}\right) = P(z > 1.592) = 0.0557$
