Question

The high temperature in Doha, Qatar is normally distributed with an average of 115.9 degrees and a standard deviation of 12 degrees.

A. What is the probability that the high temperature on a randomly chosen day in August is less than 100 degrees? Round your answer to 4 decimal places.

B. What is the probability that the high temperature on a randomly chosen day in August falls between 105 and 120 degrees? Round your answer to 4 decimal places.

Answer 1

Given,

= 115.9 , = 12

We convert this to standard normal as

P(X < x) = P( Z < x - / )

A)

P(X < 100) = P( Z < 100 - 115.9 / 12)

= P( Z < -1.325)

= 1 - P(Z < 1.325)

= 1 - 0.9074 (From Z table)

= 0.0926

B)

P(105 < X < 120) = P(X < 120) - P(X < 105)

= P(Z < 120 - 115.9 / 12) - P( Z < 105 - 115.9 / 12)

= P( Z < 0.3417) - P( Z < -0.9083)

= P( Z < 0.3417 ) - ( 1 - P( Z < 0.9083) )

= 0.6337 - ( 1 - 0.8181 )

= 0.4518