Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 20 minutes. A researcher observed 7 students who entered the library to study. Round all answers to 6 decimal places where possible. What is the distribution of ∑x∑x? ∑x∑x ~ N(,) If one randomly selected student is timed, find the probability that this student's time will be between 41 and 49 minutes.  For the 7 students, find the probability that their average time studying is between 41 and 49 minutes.

MATLAB: An Introduction with Applications
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chapter test , question 8, part 1

Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 20 minutes. A researcher observed 7 students who entered the library to study. Round all answers to 6 decimal places where possible.

  1. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
  2. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 49 minutes. 
  3. For the 7 students, find the probability that their average time studying is between 41 and 49 minutes. 
Expert Solution
Step 1

We have given that a random variable X i.e, the amount of time is normally distributed with mean 45 minutes and standard deviation 20 minutes. The sample of size n is 7.

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