One data question about Normal Distribution?

Question

A snake farm advertises that 25% of their snakes are longer than 1.5m and 10% of them are longer than 2m. what is the mean length of snakes at this farm? what is the standard deviation?

please help me to solve this question. thank you! =)

Answer 1

You have enough info to generate two equations in the two unknowns of interest.

Z(L=1.5 ) = (1.5-mu)/sigma
Z(L=2.0) = (2-mu)/sigma

But, to get the Z values, you need to use the 25% and 10% as probabilities, look in the table to get the corresponding Z values for use above.

Ie, find the Z values such that:

P(Z(1.5)) = 0.85
and
P(Z(2.0)) = 0.90