Energetic Co., a battery manufacturer, claims their battery lasts for 69.83 months with a standard deviation of 10.135 months. You randomly sample 29 of these batteries. Assuming the distribution for the battery lifetime is approximately normal, what is the probability the average lifetime is greater than 68.34?

The heart rate of 20 patients in the ICU have a mean of 95.3 beats per minute and a standard deviation of 19.6 beats per minute. Are heart rates from the ICU patients unusual given a normal heart rate has a mean of 72 beats per minute? What is the t-stastic?

The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.8 pounds with a standard deviation of 1.05 pounds. In a recent study, a group of 45 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.73 pounds after one week. If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 45 individuals will be 1.73 pounds or more? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.75 pounds with a standard deviation of 1.02 pounds. In a recent study, a group of 60 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.9 pounds after one week. If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 60 individuals will be 1.9 pounds or less? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.