I need help with my attached statistics questions.

Find the zscore for the given shaded region under the standard normal distribution. Round your answer to two decimal places. Shaded Area = 0.? Z-SCDFE = Product lifespan: A manufacturer knows that their items have a normally distributed Lifespan, with a mean of 10.6 years, and standard deyiation of 1.3 years. If you randomly purchase one item, what is the probability it will last longer than 12 years? Round your answer to three decimal places. A population of values has an unknown distribution with / = 147 and o = 62.3. You intend to draw a random sample of size n = 165. What is the mean of the distribution of sample means? (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? O. = (Please report your answer accurate to 2 decimal places.)A random variable is not normally distributed, out it is mound shaped. It has a mean or 'IU and a standard deviation of 4. If you take a sample of size 15, can you say what the shape of the sampling distribution for the sample mean is? lllinihy? {I} If the sample size is 15, then you can say the sampling distribution of the sample mean is normally distributed since the sample size is less than 35. {I} If the sample size is 15, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 35. {I} If the sample size is 15, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 35. For a sample of size 15, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary. #13:: UK: If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? Why? {I} If the sample size is 35, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 35. {I} If the sample size is 35, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 35. {I} If the sample size is 35, then you can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 35. For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary. #13:: E: A random 1yariable is normally distributed. It has a mean of 253 and a standard deviation of 1?. If you take a sample of size it], can you say 1iyhat the shape of the sampling distribution for the sample mean is? Why? {I} If the sample size is it], then you can say the sampling distribution of the sample mean is normally distributed since the 1variable is normally distributed. {1} If the sample size is it], then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30. {:2- If the sample size is it], then you can't say anything about the sampling distribution of the sample mean, since the population of the random yariable is not normally distributed and the sample size is less than 3D. For a sample of size i, state the mean of the sample mean and the standard deyiation of the sample mean. Found to two decimal places if necessary. F's: 5:3: For a sample of size ii], find the probability that the sample mean is more than 152. For: . 251} = If you take a sample of size 3?, can you say 1.yhat the shape of the distribution of the sample mean is? Why? {I} If the sample size is 3?, then you can say the sampling distribution of the sample mean is normally distributed since the 1variable is normally distributed. {I} If the sample size is 3?, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 3D. {I} If the sample size is 3?, then you can't say anything about the sampling distribution of the sample mean, since the population of the random yariable is not normally distributed and the sample size is greater than 3D. For a sample of size 3?, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary. Hz: GE: For a sample of size 3?, find the probability that the sample mean is more than lli } 252] = The heights of ten-year-old males are normally distributed with a mean of 55.4 inches and a standard deviation of 5.3 inches. If a pediatrician selects a random sample of 49 ten- year-old males from his patient population, what is the probability that the mean height of this sample will be greater than 56 inches? Round your answer to at least three decimal placesThe amount of detergent dispensed into bottles of liquid laundry detergent bottles for a particular brand is normally distributed with a mean of 86.1 ounces with a standard deviation of 1.4 ounces. If eighteen bottles are randomly chosen from the factory, what is the probability that the mean fill is more than 87.1 ounces? Round your answer to at least three decimal places. If eighteen randomly selected bottles had a mean of 87.1 oz, should the machine dispensing the detergent be recalibrated? Yes vThe average production cost for major movies is as million dollars and the standard deviation is III] million dollars. Assume the production cost distribution is normal. Suppose that If randomly,r selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible. a. For a single randomly selected movie, find the probabilitv that this movie's production cost is between 51 and End million dollars. b. For the group of I" movies, find the probability.r that the average production cost is between Ed and as million dollars. c. For part b, is the assumption of a normal distribution necessary? =13} 'fes=II._Ii= Ho Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1.4 month. 16 randomly selected people were asked what age they learned to walk. Flound all answers to 4 decimal places where possible. a. What is the probability that one randomly selected person learned to walk when the person was between 1.5 and 11 months old? b. For the 15 people. find the probability that the average age that they learned to walk is between 10.5 and 12 months old. c. For part b, is the assumption that the distribution is normal necessary? =II._IS= Moi} "res d. Find the IQR for the average first time walking age for groups of 15 people. Round to two decimal places. L11 = months I113 = months IQR: months Airlines tend to oyerbook their flights because they assume a certain percentage of people will be 'no shows' due to change in plans or late connecting flights. A recent study suggested that 34% of people actually show up for their flight on time. A random sample of 221 booked passengers is taken and whether or not they showed up on time is recorded for each of them. The Central Limit Theorem for proportions says that the sampling distribution of the proportion of people who show up on time for their flight will haye a Normal shape. {a} Give the center and standard error for the sampling distribution of proportions. Round to four decimal places as needed. mean = and standard error = {b} What is the probability that at least 92% of the randomly selected booked passengers showed up on time? Fiji 2 13.92] = {c} What is the probability that between 82% and 91% of the randomlyr selected booked passengers showed up on time? Prose g is g 1191) = {d} Is 33% an unusually low percentage of booked passengers that show up on time for their flight in a sample of 221? - Since its 2-score = , 33% an unusuallyr lowr percentage of booked passengers that show up on time for their flight in a sample of 221. e} Is 23% an unusually low percentage of booked passengers that show up on time for their flight in a sample of 221? I Since its z-score = , 23% an unusually low percentage of booked passengers that show up on time for their flight in a sample of 221. The population of weights of a particular fruit is normally distributed, with a mean of 577 grams and a standard deviation of 8 grams. If 23 fruits are picked at random, then 6% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.According to one website, approximately 81% of Americans celebrate Easter. Suppose you ask 81 of your friends if they celebrate Easter. Find the probability that more than 84% of your friends celebrate Easter. Round to 3 decimal places