13. The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If he is willing to replace only 5% of the motors that fail, how long a guarantee should he offer? Assume that the lifetime of a motor follows a normal distribution.

In a random sample of 29 residents living in major cities on the West Coast (Group 1) and 29 residents living in major cities on the East Coast (Group 2), each individual was asked their age. The results can be seen in the table below. The population standard deviation of the age in West Coast cities is known to be 11.2 years and in East Coast cities is known to be 9.3 years. Assume the populations are normally distributed. Run a test at a 0.05 level of significance to test if west coast cities are, on average, older. West Coast (Group 1) East Coast (Group 2) 25 34 47 45 18 37 38 20 30 19 50 26 52 79 61 46 40 29 22 55 34 23 35 35 55 36 60 51 68 41 20 50 33 32 36 38 37 26 42 44 60 19 71 28 54 27 20 18 45 30 52 20 34 22 57 43 64 62       Enter the P-Value - round to 4 decimal places. Make sure you put…

5. For a certain disease, 40% of untreated patients can be expected to improve within a week. We observe a population of 80 untreated patients and record the percentage who improve within one week. According to the Central Limit Theorem, such percentages are approximately normally distributed. Find the mean and standard deviation of this normal distribution. Round the standard deviation to two decimal places.

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean ? = 81 and standard deviation ? = 26. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)   (a) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 125 (borderline diabetes starts at 125)