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

SOLUTION:

From given data,

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.

		( - )2
99	99.25	(99 - 99.25)2 = 0.0625
92	99.25	(92 - 99.25)2 = 52.5625
96	99.25	(96 - 99.25)2 = 10.5625
110	99.25	(110- 99.25)2 = 115.5625
= 397		( - )2 = 178.75

Sample size = = 4

Mean = = / = 397 / 4 = 99.25

Standard deviation = = = = 6.68487

z = ( - ) /

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).

P(90 g or less) = P(< 90 )

P(< 90 ) = P( z < (90 - 99.25) / 6.68487 )

= P( z < -9.25 / 6.68487 )

= P( z < -1.38 )

=  0.08379

P(90 g or less) =  0.08379