The average starting salary for this year's graduates at a large university (LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed.a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400? b. What is the probability that a randomly selected LU graduate will have a salary of exactly $30,400? c. Individuals with starting salaries of less than $15600 receive a low income tax break. What percentage of the graduates will receive the tax break? d. If 189 of the recent graduates have salaries of at least $32240, how many students graduated this year from this university? Question 3 The College Board reported the following mean scores for the three parts of the SAT (The World Almanac, 2009):Critical reading 502Mathematics 515Writing 494Assume that the population standard deviation on each part of the test is 100.a) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical reading part of the test?b) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Compare this probability to the value computed in part (a).
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The average starting salary for this year's graduates at a large university (LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed.
a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400?
b. What is the probability that a randomly selected LU graduate will have a salary of exactly $30,400?
c. Individuals with starting salaries of less than $15600 receive a low income tax break. What percentage of the graduates will receive the tax break?
d. If 189 of the recent graduates have salaries of at least $32240, how many students graduated this year from this university?
Question 3
The College Board reported the following
Critical reading 502
Mathematics 515
Writing 494
Assume that the population standard deviation on each part of the test is 100.
a) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical reading part of the test?
b) What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Compare this probability to the value computed in part (a).
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Question 1 :
Average starting salary ( ) = $20,000
Std. deviation of starting salary ( ) = $8,000
Starting salary follows normal distribution
To find :
a ) Prob. that randomly selected graduate will have starting salary at least $30,400
b ) Prob. that randomly selected graduate will have starting salary exactly $30,400
c ) % of graduates receive the tax break for starting salary of less than $15600
d ) How many students graduated out of 189 having salaries of at least $32240
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