A random sample of size is taken from a normal population having a mean of and a

Question

A random sample of size is taken from a normal population having a mean of and a standard deviation of 3. A second random sample of size 36 is taken from a different normal population having a mean of 70 and a standard deviation of 6. Find the probability that the sample mean computed from the 81 measurements will exceed the sample mean computed from the 36 measurements by at least 13.8 but less than 15.8 Assume the difference of the mean to be measured to the The probability is (Round to four decimal places as needed.)

Explanation / Answer

for first batch

random sample size = 81

mean u1= 85

standard deviation s1 = 3

from second batch,

random sample size (n2) = 36

mean u2= 70

standard deviation s2 = 6

mean difference between two samples to be (13.8<dx<15.8)

dx = 2

Now combined proportion or normal distribution is

mean = X-Y = 5

combined std dev (s) = 6.708

P( z > ((X-Y)-dx) / s)

= p ( z > (5- 2) / 6.708 )

= p(z > 3/6.708)

= p( Z > 0.4472)

from z table

p = 0.6736

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