Answer:
(a) P(X<51) = 50.0%
(b) P(X<45) = 15.1%
(c) P(X>45) = 84.9%
Step-by-step explanation:
Mean weight (μ) = 51 pounds
Standard deviation (σ) = 5.8 pounds
The z-score for any given weight, 'X', is given by the following expression;
a) P(X<51)
Since 51 pounds is exactly the mean weight, 50% of the dogs weight more than 51 pounds while 50% weight less than 51 pounds.
P(X<51) = 50.0%
b) P(X<45)
The z-score for X=45 is:
A z-score of -1.034 is equivalent to the 15.06-th percentile in a normal distribution. Therefore:
P(X<45) = 15.1%
c) P(X>45)
P(X>45) = 100% - P(X<45) = 100% - 15.1%
P(X>45) = 84.9%