The mean temperature in downtown Los Angeles is 663 degrees

The mean temperature in downtown Los Angeles is 66.3 degrees Fahrenheit with a standard deviation of 8 degrees Fahrenheit. Assume that temperature readings are normally distributed.

Find the probability that the temperature in downtown L.A. is between 50.2 and 82.2 degrees Fahrenheit any given day.

a) 0.9761 b) 0.0222 c) 0.9539 d) 0.0076 e) 0.9354

Find the probability that the temperature in downtown L.A. is greater than 85.2 degrees Fahrenheit any given day.

a) 0.9909 b) 0.7568 c) 0.2432 d) 0.9187 e) 0.0091

Find the probability that the temperature in downtown L.A. is less than 78.22 degrees Fahrenheit any given day.

a) 0.9319 b) 0.0601 c) 0.4569 d) 0.5431 e) 0.3356

Solution

Normal Distribution
Mean ( u ) =66.3
Standard Deviation ( sd )=8
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 50.2) = (50.2-66.3)/8
= -16.1/8 = -2.0125
= P ( Z <-2.0125) From Standard Normal Table
= 0.02208
P(X < 82.2) = (82.2-66.3)/8
= 15.9/8 = 1.9875
= P ( Z <1.9875) From Standard Normal Table
= 0.97657
P(50.2 < X < 82.2) = 0.97657-0.02208 = 0.9545 ~ 0.9539              
          
b)
P(X > 85.2) = (85.2-66.3)/8
= 18.9/8 = 2.3625
= P ( Z >2.363) From Standard Normal Table
= 0.0091                  
c)
P(X < 78.22) = (78.22-66.3)/8
= 11.92/8= 1.49
= P ( Z <1.49) From Standard Normal Table
= 0.9319