s tan dard deviation(a) = 348 s tan dard deviation(o) = 112 Required probability is P x< 650 Required probability is P( X > 100 -() = P 650–p 100- = P( 650-789 100-70 Z > 348 112 = P(Z < -2. 08) = P(Z > 1.34) from Z-table = 0. 0901 from Z– table = 0.0188 The probability that the mean price is less than 650 is 0.0188. b) Given, sample size(n) = 42 mean(u) = 10 s tan dard deviation(6) = 13 Required probability is P < 15 = P -- ) - r(2- = P 10 < Z < 15- 15-10 = P(-0. 50 < Z < 2. 49) -0. 50 = 0. 9936 – 0. 3085 (from Z – table = 0. 6851 The probability that the mean no.of hours a week spent playing video games is between 9 and 15 is 0. 6851. II
s tan dard deviation(a) = 348 s tan dard deviation(o) = 112 Required probability is P x< 650 Required probability is P( X > 100 -() = P 650–p 100- = P( 650-789 100-70 Z > 348 112 = P(Z < -2. 08) = P(Z > 1.34) from Z-table = 0. 0901 from Z– table = 0.0188 The probability that the mean price is less than 650 is 0.0188. b) Given, sample size(n) = 42 mean(u) = 10 s tan dard deviation(6) = 13 Required probability is P < 15 = P -- ) - r(2- = P 10 < Z < 15- 15-10 = P(-0. 50 < Z < 2. 49) -0. 50 = 0. 9936 – 0. 3085 (from Z – table = 0. 6851 The probability that the mean no.of hours a week spent playing video games is between 9 and 15 is 0. 6851. II
s tan dard deviation(a) = 348 s tan dard deviation(o) = 112 Required probability is P x< 650 Required probability is P( X > 100 -() = P 650–p 100- = P( 650-789 100-70 Z > 348 112 = P(Z < -2. 08) = P(Z > 1.34) from Z-table = 0. 0901 from Z– table = 0.0188 The probability that the mean price is less than 650 is 0.0188. b) Given, sample size(n) = 42 mean(u) = 10 s tan dard deviation(6) = 13 Required probability is P < 15 = P -- ) - r(2- = P 10 < Z < 15- 15-10 = P(-0. 50 < Z < 2. 49) -0. 50 = 0. 9936 – 0. 3085 (from Z – table = 0. 6851 The probability that the mean no.of hours a week spent playing video games is between 9 and 15 is 0. 6851. II
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a) Given,
c)
Given,
sample size(n) = 27
mean(µ) = 789
s tan dard deviation(6) = 348
sample size(n) = 25
mean(u) = 70
s tan dard deviation(o) = 112
Required probability is P( x < 650
Required probability is P( x > 100
-()
650-u
= P
100-p
= P
= P| Z <
650-789
348
100-70
112
= P( Z >
= P(Z < -2. 08)
= P(Z > 1.34)
= 0. 0188
from Z – table
= 0, 0901
from Z – table
The probability that the mean price is less than 650
is
0. 0188.
b) Given,
sample size(n) = 42
теan(и) 3D 10
s tan dard deviation(6) = 13
Required probability is P
9 < i < 15
9-u
15-u
=
= P 9-10 <Z< 15-10
13
= P(-0.50 < Z < 2.49)
= P Z < 2.49 -
Z< -0. 50
= 0. 9936 – 0. 3085 (from Z – table
= 0.
= 0., 6851
The probability that the mean no.of hours
a week spent playing video games is between
9 and 15 is 0. 6851.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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