The time spent studying (in hours) for the final exam by students in a certain university has unknown mean μ and standard deviation 8 hours. A random sample of 4 students was taken to guess the mean study time of all students in the university. What is the (approximate) probability that the sample mean X differs from the population mean u by less than 4 hours? That is, approximate P(|X − µ| < 4). (Hint: Recall that |x| ≤ a means that –a ≤ x ≤ a.) -

MATLAB: An Introduction with Applications
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Problem Solving. Solve the following problems. No immediate rounding. Round off final answers to three decimal places.
The time spent studying (in hours) for the
final exam by students in a certain university
has unknown mean μ and standard deviation
8 hours. A random sample of 4 students was
taken to guess the mean study time of all
students in the university. What is the
(approximate) probability that the sample
mean X differs from the population mean μ
by less than 4 hours? That is, approximate
P(|X − µ| < 4). (Hint: Recall that |x| ≤ a
means that a ≤ x ≤ a.)
-
-
Answer:
Transcribed Image Text:The time spent studying (in hours) for the final exam by students in a certain university has unknown mean μ and standard deviation 8 hours. A random sample of 4 students was taken to guess the mean study time of all students in the university. What is the (approximate) probability that the sample mean X differs from the population mean μ by less than 4 hours? That is, approximate P(|X − µ| < 4). (Hint: Recall that |x| ≤ a means that a ≤ x ≤ a.) - - Answer:
Suppose a company repacks cereal with the
use of a machine that is calibrated so that the
weight of cereal dispensed in a box is
normally distributed with mean 0.40kg and
variance 0.01kg², although the weight stated
in the cereal box is 0.45kg. For quality
control purposes, suppose a random sample
of 15 cereal boxes is taken. What is the
probability of selecting a random sample with
mean weight less than the advertised weight?
Answer:
Transcribed Image Text:Suppose a company repacks cereal with the use of a machine that is calibrated so that the weight of cereal dispensed in a box is normally distributed with mean 0.40kg and variance 0.01kg², although the weight stated in the cereal box is 0.45kg. For quality control purposes, suppose a random sample of 15 cereal boxes is taken. What is the probability of selecting a random sample with mean weight less than the advertised weight? Answer:
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