An electrical company claims that the average life of the bulbs it manufactures is 1 300 hours with a standard deviation of 260 hours. If a random sample of 110 bulbs is chosen, what is the probability that the sample mean will be: a. greater than 1 160 hours? b. less than 1 260 hours? c. between 1 160 and 1 260 hours?
An electrical company claims that the average life of the bulbs it manufactures is 1 300 hours with a standard deviation of 260 hours. If a random sample of 110 bulbs is chosen, what is the probability that the sample mean will be: a. greater than 1 160 hours? b. less than 1 260 hours? c. between 1 160 and 1 260 hours?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:Example
The average number of Facebook (FB) friends of the Senior High School learners in South Cotabato is 2, 896 with a
standard deviation of 17. Assume that the variable is normally distributed. (a) If a learner is selected, what is the
probability that he or she has more than 2 900 FB friends? (b) If 69 learners are randomly selected, what is the probability
that their average FB friends is less than 2, 900?
Solution to (a)
Solution to (b)
Solution
1. Identify the given u = 2 896, o = 17
X = 2 900, n=69
P (X <2 900)
Steps
Steps
1. Identify the
given information.
Solution
µ = 2 896
a = 17
X = 2 900
P (X > 2 900)
information.
2. Identify what is
2. Identify what is
asked for.
3. Identify the
formula to be
asked for.
3. Identify the
formula to be used.
z =
z-쁘 (to
standardize 3000
since we're dealing
with individual data)
In
4. Solve the
problem.
used.
4. Solve the
problem.
2 900 - 2896
z=-
17
2900 – 2896
17
= 0.24
(using the z-table,
area to the left of the
curve)
P(X>2900)=P(X>0.24)
-1 - 0.5948
V69
=1.95
(using the z-table,
area to the left of
the curve)
P (X > 2 900)
P (X > 1.95)
=1- 0.97441= 0.03
So, the probability
that the average
number of FB
friends of 69
=0.4052
5. State the final
So, the probability
5. State the final
answer.
answer.
that a student has
more than 2 900 FB
friends is 40.52%.
randomly selected
learners is 3%.
Transcribed Image Text:АCTIVITY
An electrical company claims that the average life of the bulbs it manufactures is 1 300 hours with a standard deviation
of 260 hours. If a random sample of 110 bulbs is chosen, what is the probability that the sample mean will be:
a. greater than 1 160 hours?
b. less than 1 260 hours?
c. between 1 160 and 1 260 hours?
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