Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 12 min and variance 36 min?. (a) What are the values of a and ß? a = %3D (b) What is the probability that a student uses the terminal for at most 21 min? (Round your answer to three decimal places.) (c) What is the probability that a student spends between 15 and 27 min using the terminal? (Round your answer to three decimal places.)

Suppose the horses in a large stable have a mean weight of 1128⁢lbs, and a standard deviation of 58lbs. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 10⁢lbs if 37 horses are sampled at random from the stable? Round your answer to four decimal places.

The mean points obtained in an aptitude examination is 179points with a variance of 225.   What is the probability that the mean of the sample would differ from the population mean by less than 2.5 points if 77exams are sampled? Round your answer to four decimal places.

Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 12 min and variance 36 min². (a) What are the values of a and B? α = B = (b) What is the probability that a student uses the terminal for at most 18 min? (Round your answer to three decimal places.) (c) What is the probability that a student spends between 15 and 27 min using the terminal? (Round your answer to three decimal places.)

The mean weight of an adult is 71 kilograms with a variance of 100.   If 181 adults are randomly selected, what is the probability that the sample mean would differ from the population mean by less than 1.2 kilograms? Round your answer to four decimal places.

The next six questions refer to the following scenario: A random sample of 25 students were asked to self-identify as "statistics-lovers" or "statistics-adorers." 16 students self-identified as "lovers" and 9 students as "adorers." Below table summarizes the mean of a statistics test and standard deviation that was given after the self-identification. Test the following hypothesis at alpha=5% (0.05). HO: Mean Statistics Lovers = Mean Statistics Adorers HA: Mean Statistics Lovers Mean Statistics Adorers You can assume equal variance.

Suppose a batch of steel rods produced at a steel plant have a mean length of 178 millimeters, and a standard deviation of 12 millimeters. If 76 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.56 millimeters? Round your answer to four decimal places.

Question B1 Jessie is a doctor at a clinic. Her consultation times (X) on patients are normally distributed with a mean of 7 minutes and a standard deviation of 1.2 minutes. (a) Find the probability that she spends 5.5 minutes to 6.4 minutes for consulting a patient. Correct your final answer to 4 decimal places.