Answer to Question #204751 in Statistics and Probability for safi

Question #204751

f X is a normally distributed random variable with a mean of 45 and a standard deviation of 8, find the following probabilities: a. P(X ">"> 50). b. P(X < 32). c. P(37 < X < 48). d. P(X = 45).


1
Expert's answer
2022-01-10T14:45:23-0500

"\\mu=45 \\\\\n\n\\sigma = 8"

a.

"P(X>50) = 1 -P(X<50) \\\\\n\n= 1 -P(Z< \\frac{50-45}{8}) \\\\\n\n= 1 -P(Z< 0.625) \\\\\n\n= 1 -0.7340 \\\\\n\n= 0.2660"

b.

"P(X<32) = P(Z< \\frac{32-45}{8}) \\\\\n\n= P(Z< -1.625) \\\\\n\n= 0.0520"

c.

"P(37<X<48) = P(X<48) -P(X<37) \\\\\n\n= P(Z< \\frac{48-45}{8}) -P(Z< \\frac{37-45}{8}) \\\\\n\n= P(Z< 0.375) -P(Z< -1) \\\\\n\n= 0.6461 -0.1586 \\\\\n\n= 0.4875"

d.

P(X=45) = 0

Because there is an uncountable infinite number of a value of X, therefore the probability of each individual value is zero.


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