A population of values has a normal distribution with mu 524...

A population of values has a normal distribution with mu =52.4 and sigma =72.7. a. Find the probability that a single randomly selected value is between 48.3 and 50.4. Round your answer to four decimal places. n=205 A population of values has a normal distribution with u = 52.4 and o = 72.7. a. Find the probability that a single randomly selected value is between 48.3 and 50.4. Round your answer to four decimal places. P(48.3< X < 50.4) = b. Find the probability that a randomly selected sample of size n = 205 has a mean between 48.3 and 50.4. Round your answer to four decimal places. P(48.3< M < 50.4) =

Transcript

00:01 This problem says a population of values has a normal distribution with a mean of 28 and a standard deviation of 39 .5 and our first question wants us to find the probability that a single randomly selected value is less than 29 .9 rounding to four decimal places and since we're dealing with a normal distribution we can use normal cdf in our calculator to get this probability and for normal cdf we have to list four values starting with the lower bound and the upper bound that we want the probability between and here we want to be less than 29 .9 so that would be our upper bound and to make sure that we include everything to the left or less than 29 .9 in our distribution we'll use negative infinity for the lower bound and then we follow that with the mean and the standard deviation of our distribution which was given as 28 with a standard deviation of 39 .5 and when we evaluate here in our calculator to get our probability and round to four decimal places we get the result of zero point five one nine two and then for our question for b we are asked to find the probability that a randomly selected sample of size n equals 66 has a mean less than 29 .9 also rounding to four decimal places and to find our probability here since our population was normally distributed we can treat our sampling distribution as approximately normal as well which means we can still use normal cdf in our calculator to get our probability and we still start off with the lower bound and upper bound and we still want to be less than 29 .9 so that will be our upper bound going down to negative infinity again for the lower bound to make sure we include everything to the left but now we follow with the mean of the sampling distribution and standard deviation of the sample mean and the mean of the sampling distribution is equal to the mean of the population so that stays 28, but the standard deviation of the sample mean is the standard deviation of the population divided by the square to the sample size n...

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