  Chapter: Normal Distribution The running time for videos submitted to Youtube in a given week is normally distributed with μ=390 seconds and standard deviation σ = 148 seconds. A) If a single video is randomly selected, what is the probability that the running time of the video exceeds 6 minutes (360 seconds)?B) Suppose that sample of 40 videos is selected. What is the probability that the mean running time of the sample exceeds 6 minutes? Must show which tables were used, if it's area of the left, and a bell curve or the like. (I have the answer, it's just that I would like better help understanding how to do the probelm and so it matches the answer I have for my book, as the answers I got before didn't match so I just want to be I know how to do the steps correctly. So it's supposed to be .5803 and normalcdf (360, 1E99, 390, 148)=.5803162711 for part A, and for part B it's .9001 and normalcdf (360, 1E99, 390, 148/√(40))=.9000793931. Thank you)

Question

Chapter: Normal Distribution

The running time for videos submitted to Youtube in a given week is normally distributed with μ=390 seconds and standard deviation σ = 148 seconds.

A) If a single video is randomly selected, what is the probability that the running time of the video exceeds 6 minutes (360 seconds)?

B) Suppose that sample of 40 videos is selected. What is the probability that the mean running time of the sample exceeds 6 minutes?

Must show which tables were used, if it's area of the left, and a bell curve or the like.

(I have the answer, it's just that I would like better help understanding how to do the probelm and so it matches the answer I have for my book, as the answers I got before didn't match so I just want to be I know how to do the steps correctly. So it's supposed to be .5803 and normalcdf (360, 1E99, 390, 148)=.5803162711 for part A, and for part B it's .9001 and normalcdf (360, 1E99, 390, 148/√(40))=.9000793931. Thank you)

Step 1

The normal distribution:

A continuous random variable X is said to follow normal distribution if the probability density function of X is,

Step 2

The standard normal distribution:

A standard normal variable, the value of which is usually denoted by z, is a normal random variable with mean μ = 0 and standard deviation σ = 1. The normal variable X can be standardized using the formula:

Step 3

Calculation for part (A):

Here, let X denotes the running time of a single randomly selected video (seconds); μ = 390, σ = 148.

The probability tha...

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