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Answer:
Probability is 0.97725
Step-by-step explanation:
Given: Mean volume =12.1 ounces ,standard deviation=0.05
and 10 volumes are selected i.e no of observation or samples.
To find : calculate probability for fluid less than the 12 ounces.i.e P(X<12) with normal distribution probability .
Solution:
Given that data is independent normal random variables , which depends upon mean ,variance and the Standard Z-score .
Hence we have ,
Mean=12.1
Variance =square of (standard deviation).
Normal distribution is given by ,
N(mean,variance)
As there are 10 cans with mean 12.1 and variance=(0.05)^2=0.025.
Normal distribution probability is given by sum of independent normal random variables.
Using the notation as P(X-Y>0)
I.e. P(X>Y)
finding the probability of X greater than Y i.e.(12.1>12) ounces .
with same standard deviation we get,
X-Y ⇒N(12.1-12,0.0025)⇒N(0.1,0.0025).
=P(X-Y)
=P(X-Y>0)
=P(Z>)
=P(Z>-2)
=P(Z<2).
=0.97725.
Using the Z- table refer the normal probability Z-table.
