Question

An adult female of species felis catus has given birth to five individuals. The birth weight of the first four young, in grams, are x = 99, 92, 96, 110. Assuming the birth weights of felis catus are normally distributed, what is the probability that the fifth young has a birth weight of 90g or less? (This must be expressed as a number between 0 and 1).

Answer 1

Consider X denotes birth weight of adult of female of species felis catus.

Since the distribution of X is normally distribution.

X ~ N ( mu, Sigma²)

E(X) = mu and SD(X) =sigma

X	(X-Xbar)^2
99	0.0625
92	52.5625
96	10.5625
110	115.5625
397	178.75

E(X) = 99.25 and SD(X) = 7.7190

P ( fifth Young has a birth weight of 90 g or less) = P ( X < = 90)

since Z = (X- E(X)) / SD(X) ~ N(0,1).

From normal probability table

P ( Z <= -1.1983) = 0.1154

P( Fifth young has a birth weight of 90 g or less) = 0.1154