b) Now take an SRS of 50 students who took the test. What is the probability that the mean score of these students is 22 or higher? c) What is the probability that the mean score of an SRS of 100 students is 22 or higher? 5. Prices of homes in Raleigh, North Carolina are Normally distributed with a mean of $231,600 and a standard deviation of $38,550. a) What is the probability that a randomly selected home is worth more than $300,000? b) Take an SRS of 5 homes. What is the probability that the mean price of these homes is more than $300,000? c) What is the probability that the mean price of an SRS of 75 homes is more than $300,000? d) Why has the probability decreased so dramatically from part (a) to part (c)? 6. Charlotte, North Carolina has a mean annual rainfall of 43 inches, with a standard deviation of 4.2 inches. We can assume that the amount of rainfall is Normally distributed. a) What is the probability that, in a randomly selected year, Charlotte will receive between 40 and 46 inches of rain? bj A UNCC student attends college in Charlotte for four years. What is the probability that the mean rainfall in these 4 years will be between 40 and 46 inches? c) Why has the probability increased so dramatically from part (a) to part (b)? 7. The weight of fully-grown male German Shepherds is Normally distributed with a mean of 76 pounds and a standard deviation of 11 pounds. a) Find the probability that a randomly selected German Shepherd will weigh less than 68 pounds. b) Find the probability that an SRS of 25 German Shepherds will have a mean weight less than 68 pounds. c) Explain why the probability has decreased from part (a) to part (b)