Thread: Normal Distribution problem

Hi There

I got stuck with below problem on Normal Distribution:

A forestry nursery in the Bay of Plenty plants Douglas fir seedlings. Those that survive are measured after five years, and it is found that their diameters are normally distributed, with a mean of 22 cm and a standard deviation of 2 cm.
Two trees are chosen at random.

• Calculate the probability that both tree measures under 20cm.
• Calculate the probability that one tree measures under 20cm and the other measures over 20 cm.

Kindly help me through this problem, I shall be very thankful to you.
Many thanks in advance.
Parveen

Originally Posted by Parveen Kaur

Hi There

I got stuck with below problem on Normal Distribution:

A forestry nursery in the Bay of Plenty plants Douglas fir seedlings. Those that survive are measured after five years, and it is found that their diameters are normally distributed, with a mean of 22 cm and a standard deviation of 2 cm.
Two trees are chosen at random.

• Calculate the probability that both tree measures under 20cm.
• Calculate the probability that one tree measures under 20cm and the other measures over 20 cm.

Kindly help me through this problem, I shall be very thankful to you.
Many thanks in advance.
Parveen

20cm is 1 sd below the mean, so it corresponds to a z-score of -1. Look this
up in a table of the standard normal distribution to find that the probability
of getting a z of less than -1 is 0.1587.

That both trees are under 20cm has probability 0.1587^2 ~= 0.025

That one is under and the other over 20cm means either the first is under
and the second over or the first is over and the seond under so the required
probability is 0.1587*(1-0.1587) + (1-0.1587)*0.1587 ~= 0.267

RonL

Hi RonL

I understand the problem now from your explanation.
Many thanks to you for your help.
You are genious!