Question

Historically, the daily average temperature in Waterloo in November has been 2.3 degrees, with a standard deviation of 5 degrees. Assuming daily average temperatures are normally distributed, what is the probability that the mean of the daily average temperatures in Nov 2019 (which has 30 days) will be 5 degrees or more?

Question 8 options:

	0.4814
	0.0015
	0.2946
	0.025

Answer 1

Given that ,

mean = $\mu$ = 2.3

standard deviation = $\sigma$ = 5

n = 30

$\mu$_{$\bar x$} = 2.3

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 5/ $\sqrt$ 30 = 0.9129

P($\bar x$ >5 ) = 1 - P($\bar x$ < 5)

= 1 - P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (5 - 2.3) /0.9129 ]

= 1 - P(z < 2.96)

Using z table,    

= 1 - 0.9985

= 0.0015

probability = 0.0015

correct option =0.0015