Answer in Statistics and Probability for safi #204751
October 24th, 2022
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).
“mu=45 \nnsigma = 8”
a.
“P(X>50) = 1 -P(X<50) \nn= 1 -P(Z< frac{50-45}{8}) \nn= 1 -P(Z< 0.625) \nn= 1 -0.7340 \nn= 0.2660”
b.
“P(X<32) = P(Z< frac{32-45}{8}) \nn= P(Z< -1.625) \nn= 0.0520”
c.
“P(37<X<48) = P(X<48) -P(X<37) \nn= P(Z< frac{48-45}{8}) -P(Z< frac{37-45}{8}) \nn= P(Z< 0.375) -P(Z< -1) \nn= 0.6461 -0.1586 \nn= 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.
