Question

You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F.

1.

What is the probability that the low temperature on a given night will be between 22°F and 29°F? Include 4 decimal places in your answer.

2.

What temperature must the sleeping bag be suited such that the temperature will be too cold only 5% of the time?  Include 1 decimal places in your answer.

3.

What is the probability that on a given night the low temperature will be 32°F? Include 4 decimal places in your answer.

Answer 1

Solution :

Given that ,

mean = = 32

standard deviation = = 8

P(22< x <29 ) = P[(22-32) /8 < (x - ) / < (29-32) /8 )]

= P( -1.25< Z <-0.375 )

= P(Z <-0.375 ) - P(Z <-1.25 )

Using z table   

= 0.3538-0.1056

probability=0.2482

(b)  

Using standard normal table,

P(Z < z) = 5%

= P(Z < z) = 0.05

= P(Z < -1.64) = 0.05

z = -1.64 Using standard normal z table,

Using z-score formula  

x= z * +

x= -1.64*8+32

x= 18.9

(C)

P(X< 32) = P[(X- ) / < (32-32) / 8]

= P(z <0 )

Using z table

=0.5

probability=0.5