Question

Weights of a healthy 10-week-old domestic kitten are normally distributed with an average weight of μ = 24.5 ounces and a standard deviation of σ = 5.25 ounces.

1. What is the probability that a healthy 10-week-old kitten will weigh less than 14 ounces?

2a. What is the probability that a healthy 10-week-old kitten will weigh more than 32 ounces?

2b. If the Wilmington Humane Society has twenty healthy10-week-old kittens, about how many will weigh more than 32 ounces? Round to the nearest whole number.

3. If a 10-week-old kitten’s weight is in the bottom 10% of the distribution of weights, then it is said to be undernourished. At what weight is a 10-week-old kitten considered to be undernourished?

Answer 1

We are given the distribution here as:

Q1) The probability that a healthy 10-week-old kitten will weigh less than 14 ounces is computed here as:

P(X < 14)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we get here:

Therefore 0.0228 is the required probability here.

Q2) a) Now  the probability that a healthy 10-week-old kitten will weigh more than 32 ounces is computed here as:

P(X > 32)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we have here:

therefore 0.0766 is the required probability here.

b) The expected number of healthy10-week-old kittens that will weigh more than 32 ounces is computed here as:

= 0.0766*20

= 1.532

therefore 2 is the expected number here.

Q3) From standard normal tables, we have here:
P( Z < -1.282) = 0.1

Therefore the undernourished limit here is computed as:
= Mean - 1.282*Std Dev

= 24.5 - 1.282*5.25

= 17.7695

therefore 17.7695 ounces is the required value here.