Question

PROBABILITY

Answer the following. All applicable formulas used in the computations for this are required. Simply providing the answers will not be credited.

1. In a given region, the precipitation levels for 24-hour intervals are measured. Historical data indicate that in these 24-hour intervals, the mean precipitation is 5” while the standard deviation is 1.75”. A flood watch is issued when the precipitation exceeds 10”. Compute for the probability that a flood watch will be issued assuming that the historical observations are NORMALLY distributed.

Answer 1

Solution:

Given:In a given region, the precipitation levels for 24-hour intervals are measured. Historical data indicate that in these 24-hour intervals, the mean precipitation is 5” while the standard deviation is 1.75”.

That is: Mean =

Standard Deviation =

A flood watch is issued when the precipitation exceeds 10”.

We have to find:

P( a flood watch will be issued) = .......?

That is we have to find:

P( X > 10) ...........?

Find z score:

Thus we get:

P( X > 10 )= P( Z > 2.86)

P( X > 10 )= 1 - P( Z < 2.86)

Look in z table for z = 2.8 and 0.06 and find area.

P( Z < 2.86) = 0.9979

Thus

P( X > 10 )= 1 - P( Z < 2.86)

P( X > 10 )= 1 - 0.9979

P( X > 10 )= 0.0021

the probability that a flood watch will be issued is 0.0021