Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 46 minutes and standard deviation 16 minutes. A researcher observed 17 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N 46 16 b. What is the distribution of ? - N 46 15.058 x) 0³ c. What is the distribution of Σα? Σα - N 782 ✓4352 X OF d. If one randomly selected student is timed, find the probability that this student's time will be between 47 and 50 minutes. 0.0785 X

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B C AND D ONLY PLEASE
8:00 ✓
5G
Suppose that the amount of time that students spend
studying in the library in one sitting is normally
distributed with mean 46 minutes and standard
deviation 16 minutes. A researcher observed 17
students who entered the library to study. Round all
answers to 4 decimal places where possible.
a. What is the distribution of X? X - N 46
16
OB
b. What is the
distribution of ? N 46
15.058: X
08
c. What is the distribution of Σx? Σ - N(
X
782
4352 X
d. If one randomly selected student is timed, find
the probability that this student's time will be
between 47 and 50 minutes. 0.0785
X
e. For the 17 students, find the probability that
their average time studying is between 47 and 50
minutes.
f. Find the probability that the randomly selected
17 students will have a total study time more
than 680 minutes. 0.5080
X
g. For part e) and f), is the assumption of normal
necessary? Yes No o
h. The top 20% of the total study time for groups of
17 students will be given a sticker that says
"Great dedication". What is the least total time
that a group can study and still receive a sticker?
49.2
X minutes
Hint:
myopenmath.com
Transcribed Image Text:8:00 ✓ 5G Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 46 minutes and standard deviation 16 minutes. A researcher observed 17 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N 46 16 OB b. What is the distribution of ? N 46 15.058: X 08 c. What is the distribution of Σx? Σ - N( X 782 4352 X d. If one randomly selected student is timed, find the probability that this student's time will be between 47 and 50 minutes. 0.0785 X e. For the 17 students, find the probability that their average time studying is between 47 and 50 minutes. f. Find the probability that the randomly selected 17 students will have a total study time more than 680 minutes. 0.5080 X g. For part e) and f), is the assumption of normal necessary? Yes No o h. The top 20% of the total study time for groups of 17 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? 49.2 X minutes Hint: myopenmath.com
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