SAT scores in one state is normally distributed with a mean of 1481 and a standard deviation of 88. Suppose we randomly pick 49 SAT scores from that state. a) Find the probability that one of the scores in the sample is less than 1457. P(X<1457)P(X<1457) = b) Find the probability that the average of the scores for the sample of 49 scores is less than 1457. P(¯¯¯X<1457)P(X¯<1457) =
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!
SAT scores in one state is
a) Find the probability that one of the scores in the sample is less than 1457.
P(X<1457)P(X<1457) =
b) Find the probability that the average of the scores for the sample of 49 scores is less than 1457.
P(¯¯¯X<1457)P(X¯<1457) =
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
