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PART A

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) LO USE SALT 4 = 24; 0 = 3.4 P(x 2 30) =First, to find areas and probabilities for a random variable x that follows a normal distribution with mean u = 19 and standard deviation o = 3.7 we must convert the x value to a z value. Use the formula z = * - M to convert the given x value to a z value. Find the z value, rounded to two decimal places, for x = 30 with mean a = 19 and standard deviation o = 3.7. X - 4 Z= - 19 3.7 Therefore, converted to a z value, we wish to find the P Z >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 & = 80 and standard deviation o = 30. 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.) LA USE SALT (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)Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 7.6 minutes and a standard deviation of 2.3 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.) LO USE SALT (a) the response time is between 3 and 9 minutes (b) the response time is less than 3 minutes (c) the response time is more than 9 minutesWe are asked to find the probability that the police response time will be within a certain interval of time. First, to find probabilities and areas for a random variable x that follows a normal distribution with mean # = 8.4 and standard deviation o = 2.2, we must convert the given measurements x to z values. Recall that the formula z = _ _ is used to convert x values to z values. We want to find the probability that a response time will be between 4 and 10 minutes. So, we need to convert x = 4 and x = 10 to z values. For x = 4 with # = 8.4 and o = 2.2, we have the following z value. X - H Z= - 8.4 2.2 For x = 10 with a = 8.4 and o = 2.2, we have the following z value, rounded to two decimal places. X - A - 8.4 2.2