A sample of size 115 will be drawn from a population with mean 48 and standard deviation 12 . Use the TI-83 Plus/TI-84 Plus calculator. Part: 0 / 2 Part 1 of 2 (a) Find the probability that x will be less than 45 . Round the answer to at least four decimal places. The probability that > will be less than 45 isA sample of size 30 will be drawn from a population with mean 42 and standard deviation 10. Use the TI-84 Plus calculator. (a) Is it appropriate to use the normal distribution to find probabilities for x? (b) Find the probability that x will be between 43 and 44. Round the answer to at least four decimal places. (c) Find the 36 percentile of y. Round the answer to at least two decimal places. It is appropriate to use the normal distribution to find probabilities for x. 5 The probability that & will be between 43 and 14 is The 36 percentile of x is It is not appropriate to use the normal distribution to find probabilities for x.A sample of size : will be drawn from a normal population with mean 61 and standard deviation 13 . Use the TI-84 Plus calculator. (a) Is it appropriate to use the normal distribution to find probabilities for x? (b) Find the probability that x will be between $1 and 71 . Round the answer to at least four decimal places. (c) Find the $1" percentile of x. Round the answer to at least two decimal places. It is appropriate to use the normal distribution to find probabilities for a. X 5 The probability that a will be between $1 and 71 is The $1 " percentile of x is It is not appropriate to use the normal distribution to find probabilities for x.SAT scores: Assume that in a given year the mean mathematics SAT score was 467 , and the standard deviation was 105 . A sample of 59 scores is chosen. Use the TI-84 Plus calculator. Part 1 of 5 (3) What is the probability that the sample mean score is less than 456 7 Round the answer to at least four decimal places. The probability that the sample mean score is less than 45: is X 5 Part 2 of 5 (b) What is the probability that the sample mean score is between 430 and 470 ? Round the answer to at least four decimal places. The probability that the sample mean score is between 430 and 470 is X 5 Part 3 of 5 (c) Find the 45" percentile of the sample mean. Round the answer to at least two decimal places. The +5" percentile of the sample mean is X Part 4 of 5 (d) Would it be unusual if the the sample mean were greater than 499 7 Round answer to at least four decimal places. It (Choose one) | be unusual if the the sample mean were greater than 499 , since the probability is. X Part 5 of 5 (e) Do you think it would be unusual for an individual to get a score greater than 499 ? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places. (Choose one) , because the probability that an individual gets a score greater than 499 isHigh-rent district: The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2693 . Assume the standard deviation is $ $17. A real estate firm samples 115 apartments. Use the TI-84 Plus calculator. Part 1 of 5 (a) What is the probability that the sample mean rent is greater than $ 2763 ? Round the answer to at least four decimal places. The probability that the sample mean rent is greater than $2763 is X 5 Part 2 of 5 (b) What is the probability that the sample mean rent is between $2562 and $2662 ? Round the answer to at least four decimal places. The probability that the sample mean rent is between $2362 and $2662 is X Part 3 of 5 (c) Find the 65" percentile of the sample mean. Round the answer to at least two decimal places. The 65 "percentile of the sample mean rent is S. X 5 Part 4 of 5 (d) Would it be unusual if the sample mean were greater than $2751 ? Round answer to at least four decimal places. (Choose one) v , because the probability that the sample mean is greater than $27:1 is X 5 Part 5 of 5 (e) Do you think it would be unusual for an individual to have a rent greater than $2781 ? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places. Choose one) , because the probability that an apartment has a rent greater than $2751 isElevator ride: Engineers are designing a large elevator that will accommodate 45 people. The maximum weight the elevator can hold safely is $100 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 176 pounds and standard deviation 65 pounds, and the weights of adult U.S. women have mean 166 pounds and standard deviation 74 pounds. Use the TI-84 Plus calculator. Part 1 of 3 (3) If 45 people are on the elevator, and their total weight is $100 pounds, what is their average weight? The average weight is pounds. X 5 Part 2 of 3 (b) If a random sample of 45 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded? Round the answer to at least four decimal places. The probability that the maximum safe weight will be exceeded is X Part 3 of 3 (c) If a random sample of 45 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded? Round the answer to at least four decimal places. The probability that the maximum safe weight will be exceeded is XAnnual income: The mean annual income for people in a certain city (in thousands of dollars) is 42 , with a standard deviation of 24 . A pollster draws a sample of 90 people to interview. Part 1 of 5 (a) What is the probability that the sample mean income is less than 39? Round the answer to at least four decimal places. The probability that the sample mean income is less than 39 is X Part 2 of 5 (b) What is the probability that the sample mean income is between 40 and 43 7 Round the answer to at least four decimal places. The probability that the sample mean income is between 40 and 43 is. X Part 3 of 5 (c) Find the 60"percentile of the sample mean. Round the answer to at least one decimal place. The 60" percentile of the sample mean is X 5 Part 4 of 5 (d) Would it be unusual for the sample mean to be less than 35 7 Round the answer to at least four decimal places. It (Choose one) | unusual because the probability of the sample mean being less than 35 is X 5 Part 5 of 5 (e) Do you think it would be unusual for an individual to have an income of less than 35 7 Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places. (Choose one) , because the probability that an individual has an income less than 3: is