What are the answers Part 1 of 5Page 10/29Question 11 of 20Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 40, with a standarddeviation of 28. A pollster draws a sample of 90 people to interview.(a) What is the probability that the sample mean income is less than 35?(b) What is the probability that the sample mean income is between 38 and 46?P+(c) Find the 40percentile of the sample mean.(d) Would it be unusual for the sample mean to be less than 38?(e) Do you think it would be unusual for an individual to have an income of less than 38?Part 2 of 511of 20decimal places.(a) What is the probability that the sample mean income is less than 35? Round the answer to at least fourCopyright © 2023 McGraw Hill - ALEKS® is a registered trademark of ALEKS CorporationThe probability that the sample mean income is less than 35 is"IPart 3 of 5percentile of the sample mean isThe probability that the sample mean income is between 38 and 46 isdecimal places.(b) What is the probability that the sample mean income is between 38 and 46? Round the answer to at least four(c) Find the 40th percentile of the sample mean. Round the answer to at least one decimal place.The 40thCommsese

Let us assume that denotes the annual income for people in a certain city.The mean value of X: The standard deviation of X: Sample size(Number of people interviewed): Using the concept of Central Limit Theorem, as the sample size is greater than 30, the sample mean, is .The mean value is obtained as:The sample mean is obtained as .The standard deviation of sample mean are obtained as:The standard deviation is obtained as .The probability that is less than 35 is obtained as:The probability that is less than 35 is .Note: The is obtained using the MS-excel formula "=NORMSDIST( ) and the probability value is obtained as:Probability that the sample mean income is between 38 and 46 is obtained as:The is approximately .The is obtained using the MS-excel formula "=NORMSDIST( )" and the probbaility value is obtained as:The is obtained using the MS-excel formula "=NORMSDIST( )" and the probbaility value is obtained as:The standardized z-value for percentile is obtained as:Note: The standard z-value is obtained using the MS-excel formula "=NORMSINV( )" and the z-value for percentile is obtained as:The percentile is obtained as:The percentile mean score is obtained as .The probability that the sample mean is less than 38 is obtained as:As the obtained probability is greater than, it is not unusual to have the sample mean to be less than 38.Rule of Thumb: If the probability of an event comes out to be less than, the event is said to be unusual.Note: The is obtained using the MS-excel formula "=NORMSDIST( )" and is obtained as:Probability that an individual will have the income less than 38 is obtained as:As the obtained probability is greater than , it is not unusual to have the individual income to be less than 38.Note: The is obtained using the MS-excel formula "=NORMSDIST( )" and is obtained as:Probability that the sample mean income is less than 35 is .Probability that the sample mean income is between 38 and 46 is .The percentile of mean income is No, It is not unusual to say that the value of sample mean is less than 38 for the sample of size 90.No, it is not unusual to have the individual income to be less than 38 for the sample of size 90.