Week 4 Homework 1. The students who took Mrs. Johnson's math quiz scored a mean of 51 with a variance of 46. Since the scores were low, Mrs. Johnson decided to curve the scores. If Peter had an...

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Week 4 Homework 1. The students who took Mrs. Johnson's math quiz scored a mean of 51 with a variance of 46. Since the scores were low, Mrs. Johnson decided to curve the scores. If Peter had an original score of 32 and a curved score of 68, and Rachel had an original score of 86 and a curved score of 95, what is the sum of the mean and standard deviation of the new score distribution? Round to the nearest thousandth.  2. Suppose a fair 350-sided die (numbered from 1 to 350) is rolled an infinite amount of times, and a dotplot is made of the numbers rolled. Find  the standard deviation of the dotplot. Round to 4 decimal places.  3. Sharon is debating whether or not to wait in line for donuts. She decided to use the random number generator on her calculator to make this decision. She sets the  bounds to include any real number from 1 to 5. If she gets a number that is within 0.189 of  the nearest integer, then she won’t wait in line. What is the probability that Sharon waits in line for donuts? 4. Tamara decides to follow a daily routine to grow to be 5’6’’ faster. She first drinks 4 glasses of milk, then flexes her calf muscles until she gets tired, and finally stretches her arms in the air. It takes her a mean time of 6 minutes to drink all the milk, a mean of 10 minutes to flex her calf muscles until she gets tired, and a mean of 14 minutes to stretch out her arms. If each activity is done in that order independently of each other, and they can each be represented by normal distributions with a standard deviation of 3 minutes, what is the probability that Tamara will finish her routine within 30 minutes on any given day? Round your answer to the  nearest thousandth.  5. In the most recent AP Statistics test, 15% of students scored higher than an 80, but a mere 3% scored higher than a 90. If the test scores are normally distributed, what is the positive difference of the mean and variance of the distribution?  6. Tony has failed his teacher's math test, so he decides to throw darts at a poster of his teacher's face until he first lands one on his nose. He has a fixed probability of 0.09 of doing this. Assume all throws are independent of each other.  a) What is the expected number of times that Tony must throw until he first lands a dart on his teacher's nose? Round to the nearest whole number.  b) What is the probability that he will not make the shot until the 10th shot? Round your answer to 4 decimal places.