Question

In: Statistics and Probability

The weight of chihuahuas follows a Normal distribution with mean 10.4 pounds and with a standard...

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?

Solutions

Expert Solution

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


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