Question

The average weight of a professional football player in 2009 was 248.1 pounds. Assume the population standard deviation is 30 pounds. A random sample of 38 professional football players was selected. Complete parts a through e. a. Calculate the standard error of the mean. $sigma_{ar{x}} = Box$ (Round to two decimal places as needed.) b. What is the probability that the sample mean will be less than 240 pounds? P$(ar{x} < 240) = Box$ (Round to four decimal places as needed.) c. What is the probability that the sample mean will be more than 234 pounds? P$(ar{x} > 234) = Box$ (Round to four decimal places as needed.) d. What is the probability that the sample mean will be between 252 pounds and 259 pounds? P$(252 le ar{x} le 259) = Box$ (Round to four decimal places as needed.) e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is 248.1 pounds. $Box le ar{x} le Box$ (Round to the nearest pound as needed.)

          The average weight of a professional football player in 2009 was 248.1 pounds. Assume the population standard deviation is 30 pounds. A random sample of 38 professional football players was selected. Complete parts a through e.
a. Calculate the standard error of the mean.
$sigma_{ar{x}} = Box$
(Round to two decimal places as needed.)
b. What is the probability that the sample mean will be less than 240 pounds?
P$(ar{x} < 240) = Box$
(Round to four decimal places as needed.)
c. What is the probability that the sample mean will be more than 234 pounds?
P$(ar{x} > 234) = Box$
(Round to four decimal places as needed.)
d. What is the probability that the sample mean will be between 252 pounds and 259 pounds?
P$(252 le ar{x} le 259) = Box$
(Round to four decimal places as needed.)
e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is 248.1 pounds.
$Box le ar{x} le Box$
(Round to the nearest pound as needed.)

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The average weight of a professional football player in 2009 was 248.1 pounds. Assume the population standard deviation is 30 pounds. A random sample of 38 professional football players was selected. Complete parts a through e.
a. Calculate the standard error of the mean.
sigmaarx = Box
(Round to two decimal places as needed.)
b. What is the probability that the sample mean will be less than 240 pounds?
P(arx < 240) = Box
(Round to four decimal places as needed.)
c. What is the probability that the sample mean will be more than 234 pounds?
P(arx > 234) = Box
(Round to four decimal places as needed.)
d. What is the probability that the sample mean will be between 252 pounds and 259 pounds?
P(252 le arx le 259) = Box
(Round to four decimal places as needed.)
e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is 248.1 pounds.
Box le arx le Box
(Round to the nearest pound as needed.)

Added by Andrew W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Prabhakar Kumar

08/30/2023

Step 1

Standard error of the mean: SE = σ/√n = 30/√38 ≈ 4.87 (rounded to two decimal places) Show more…

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The average weight of a professional football player in 2009 was 248.1 pounds. Assume the population standard deviation is 30 pounds. A random sample of 38 professional football players was selected. Complete parts a through e. a. Calculate the standard error of the mean. (Round to two decimal places as needed.) b. What is the probability that the sample mean will be less than 240 pounds? (Round to four decimal places as needed.) c. What is the probability that the sample mean will be more than 234 pounds? (Round to four decimal places as needed.) d. What is the probability that the sample mean will be between 252 pounds and 259 pounds? (Round to four decimal places as needed.) e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is 248.1 pounds. (Round to the nearest pound as needed.)

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Transcript

00:01 In this question, we have been given to calculate the value of standard error in the first part and we can say that sigma x bar will be equals to sigma and then it is under root of n.

00:10 So, this will be here 30 and now it is going to be under root of 38 and that is equals to 4 .87.

00:18 Now, here we can say that the value of probability such that x bar is here lesser than 240.

00:24 So, this will be here equals to probability of x bar minus mu and then it is here sigma now it will be under root of n and now it is here going to be let us write x bar which is going to be here 240 and then mu value which is basically 248 .1 and then in the denominator it is 4 .87.

00:45 So, we will be getting the value of this very expression as probability of z and that is lesser than negative 1 .66.

00:52 So, that is 0 .0 and then it is 485.

00:56 So, here we can say that it is our answer and we can put the answer inside the box and now let us see how we can obtain the answer for the third part of this very problem.

01:07 So, here in the third part we can say that probability of it will be here x bar and that is greater than 234 and that is here equals to probability of x bar minus mu and then it will be here sigma now it is under root of n.

01:22 So, this will be here greater than 234 and then it is minus it is 248 .1 and then in the denominator it is 4 .87.

01:32 So, we will be here getting the value of this very expression as probability of z and that is greater than negative 2 .89.

01:40 So, this will be here equals to 0 .99 and then it is 81.

01:45 So, we can put this very answer inside the box in order to highlight it and now let us see how we can obtain the answer for the fourth part of this very problem...

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