A random sample of n=49 observations is drawn from a population with a mean equal to 20
and a standard deviation equal to14.
a. Find the probability that x overbarx is less than 14.
b. Find the probability that x overbarx is greater than 25.
c. Find the probability that x overbarx falls between 14 and 22.
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a. The probability that x overbarx is less than 14 is ________(Round to three decimal places as needed.)
Given n = 49
mean = 20
standard deviation =14
a)
probability that x is less than 14
P( x < 14 ) = x - μ / σ / sqrt(n)
= 14 - 20 / 14/ sqrt (49)
= - 6 / 14 / 7
= -6 / 2
P( x < 14 )= -3
P ( Z<−3 )=1−P ( Z<3 )=1−0.9987=0.0013 = 0.001
b)
probability that x is greater than 25
p( x >25) = x - μ / σ / sqrt(n)
= 25 - 20 /14 sqrt(49)
= 5 /2
=2.5
P ( Z>2.5 )=1−P ( Z<2.5 )=1−0.9938=0.0062
c) probability that x falls between 14 and 22.
P ( 14 < X < 22) = ( 14 - 20 / 14/ sqrt (49) < X < 22 - 20 / 14/ sqrt (49) )
= ( -6 / 14/7 < X < 2 / 14/7 )
= ( -3 < X <1)
P ( -3 < X <1)= P ( -3 < Z <1) = 0.84
A random sample of n=49 observations is drawn from a population with a mean equal to...
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