Activity 2.2 The Average time it takes a group of senior high school students to complete a certain examination is 46.2 minutes. The Standard deviation is 8 minutes. Assume the variable is normally distributed. A. What is the probability that a random selected senior high student will complete the examination in less than 43 minutes? B. If 50 randomly selected senior high school students take the examination, what is the nrohahil

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Answer Activity 2.2, 2.3 and 2.4
Activity 2.2
The Average time it takes a group of senior high school students to complete a
certain examination is 46.2 minutes, The Standard deviation is 8 minutes. Assume he
variable is normally distributed.
A. What is the probability that a random selected senior high student will
complete the examination in less than 43 minutes?
B. If 50 randomly selected senior high school students take the examination,
what is the probability that the mean time it takes the group to complete the
test will be less than 43 minutes?
The Central Limit Theorem is of fundamental importance in statistics because
it justifies the use of normal curve methods for a wide range of problems. This theorem
applies automatically to sampling from infinite population. It also assures that no
matter what the shape of the population distribution of the mean is, the sampling
distribution of the sample means is closely normally distributed whenever n is large.
Consequently, it justifies the use of the formula z =
when computing for
the probability that X will take on a value within a given range in the sampling
distribution of X.
z =
Where X = sample mean
p = population mean
D = population standard deviation
n = sample size
Activity 2.3
The average number of milligrams (mg) of cholesterol in a cup of a
certain brand of ice cream is 660 mg, and the standard deviation is 35 ma.
Assume the variable is normally distributed.
A. If a cup of ice cream is selected, what is the probability that the
cholesterol content will be more than 670 mg?
B. I a sample of 10 cups of ice cream is selected, what is the probability
that the mean of the sample will be larger than 670 mg?
An electric company claims that the average life of the bulbs it manufactures is
1200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs
is chosen, what is the probability that the sample mean will be:
a. greater than 1 150 hours?
b. less than 1 250 hours?
Activity 2.4
Transcribed Image Text:Activity 2.2 The Average time it takes a group of senior high school students to complete a certain examination is 46.2 minutes, The Standard deviation is 8 minutes. Assume he variable is normally distributed. A. What is the probability that a random selected senior high student will complete the examination in less than 43 minutes? B. If 50 randomly selected senior high school students take the examination, what is the probability that the mean time it takes the group to complete the test will be less than 43 minutes? The Central Limit Theorem is of fundamental importance in statistics because it justifies the use of normal curve methods for a wide range of problems. This theorem applies automatically to sampling from infinite population. It also assures that no matter what the shape of the population distribution of the mean is, the sampling distribution of the sample means is closely normally distributed whenever n is large. Consequently, it justifies the use of the formula z = when computing for the probability that X will take on a value within a given range in the sampling distribution of X. z = Where X = sample mean p = population mean D = population standard deviation n = sample size Activity 2.3 The average number of milligrams (mg) of cholesterol in a cup of a certain brand of ice cream is 660 mg, and the standard deviation is 35 ma. Assume the variable is normally distributed. A. If a cup of ice cream is selected, what is the probability that the cholesterol content will be more than 670 mg? B. I a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg? An electric company claims that the average life of the bulbs it manufactures is 1200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability that the sample mean will be: a. greater than 1 150 hours? b. less than 1 250 hours? Activity 2.4
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