Question 1:

Let 3 be a random variable with a standard normal distribution. Find the indicated probability. {Round your answer to four decimal places.) m 2 .1. = Shade the corresponding area under the standard normal curve. Shade: . Click. and drag the arrows to adjust the 1.Irsilues. I Question 1 v Find the z such that 42.3% of the standard normal curve lies to the right of z. -3 -2 -1 OZ 3 Q Z= (Round your answer to 2 decimal places.)I Question E: v The lengths of pregnancies in a small mral village are normally distributed with a mean of HE! days and a standard deviation of 14 days. Let X be the length of a randomly recorded pregnancy in the village. a. What is the distribution of it? it ~ { , 1 Please show the following answers to 4 decimal places. b. If a pregnancy randomly chosen in the village, find the probability that it lasted at least 291 days. c. If a pregnancy randomly chosen in the village, find the probability that it lasted between 163 and 134 days. Please show Hie following answer to a whole day. d. The TTth percentile pregnancy length in this village is C] days. U Question 12 v Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of as inches and a standard deviation of 1.1 inches. X be the head breadth of a potential clientele. a. What is the distribution of x? it ~ {:LS] Please show the following answers to 4 decimal places. b. If a client is randomly chosen, find the probability that his head breadth is at least 3.3 inches. :1 c. If a client is randomly chosen, find the probability that his head breadth is between at: and 9.1 Please show the following answers to one decimal place. d. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1% or largest 2%. What is the minimum and maximum head breadths that will fit the clientele? Minimum and maximum = C] and C] inches. I Question 13 v Company IVE knows that replacement times for the mircowaves it produces are normally distributed with a mean of 3.9 years and a standard deviation of 1.4 years. Let X be the replacement time of a randomly selected mircowave. a. What is the distribution of x? it ~ { , 1. Please show the following answers to 4 decimal places. b. If a mircowave is randomly chosen, find the probability that it will be replaced in more than 11 .B c. If a mircowave is randomly chosen, find the probability that it will be replaced between 10.1 and Please show the following answer to 1 decimal place. d. If the company wants to provide a warranty so that only E94; of the mircowayes will be replaced before the warranty expires, what is the time length of the warranty? C] years