In: Statistics and Probability
The weight of chihuahuas follows a Normal distribution with mean 10.4 pounds and with a standard deviation of 2.1 pounds.
A) What percent of the dogs weigh more than 12 pounds?
B) What percent of the dogs weight between 9 and 12 pounds?
C) 50% of the dogs weigh more than what weight?
D) 75% of the dogs weight more than what weight?
a) P(X > 12)
= P((X - )/ > (12 - )/)
= P(Z > (12 - 10.4)/2.1)
= P(Z > 0.76)
= 1 - P(Z < 0.76)
= 1 - 0.7764
= 0.2236
b) P(9 < X < 12)
= P((9 - )/ < (X - )/ < (12 - )/)
= P((9 - 10.4)/2.1 < Z < (12 - 10.4)/2.1)
= P(-0.67 < Z < 0.76)
= P(Z < 0.76) - P(Z < -0.67)
= 0.7764 - 0.2514
= 0.525
C) P(X > x) = 0.5
or, P((X - )/ > (x - )/) = 0.5
or, P(Z > (x - 10.4)/2.1) = 0.5
or, P(Z < (x - 10.4)/2.1) = 0.5
or, (x - 10.4)/2.1 = 0
or, x = 0 * 2.1 + 10.4
or, x = 10.4
D) P(X > x) = 0.75
or, P((X - )/ > (x - )/) = 0.75
or, P(Z > (x - 10.4)/2.1) = 0.75
or, P(Z < (x - 10.4)/2.1) = 0.25
or, (x - 10.4)/2.1 = -0.67
or, x = -0.67 * 2.1 + 10.4
or, x = 8.993