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13 votes
13 votes
20. Assume that X has a normal distribution, and find the indicated probabilityThe mean is u - 60,0 and the standard deviation is o = 4.0,Find the probability that X is less than 53.0.

User Takagi Akihiro
by
2.7k points

1 Answer

20 votes
20 votes

Recall that the Normal Distribution Formula is given by the z-score:


z=(X-\mu)/(\sigma)

Where μ is the mean and σ is the standard deviation.

Substitute μ=60.0, σ=4.0, and X=53.0 into the formula:


z=(53.0-60.0)/(4.0)=-(7)/(4)

It then follows that:


P(X<53)=P(z<-(7)/(4))

Next, check this in the normal distribution table, to get:


P(X<53)=P(z<-(7)/(4))=0.0401

The answer is 0.0401.

User Lkisac
by
3.0k points
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