Question

The average daily high temperature in June in LA is 80∘F with a standard deviation of 6∘F. Suppose that the temperatures in June closely follow a normal distribution.

(a) What is the probability of observing a 76∘F temperature or higher in LA during a randomly chosen day in June?

74%

(b) What is the probability of observing a 77∘F temperature or lower in LA during a randomly chosen day in June?

31%

(c) What is the probability of observing a temperature between 77∘F and 88∘F in LA during a randomly chosen day in June?

(d) Find a temperature so that 18% of days will be warmer during June in LA.  ∘F

Answer 1

a. Here we need to find

As distribution is normal we can convert x to z

b. Here we need to find

c.

d. Here we need to find x such that

Using z table we get

So

Hence