A random sample of air temperatures in December is taken from n = 66cities in Mi

Question

A random sample of air temperatures in December is taken from n = 66cities in Minnesota. Temperature data is known to be normally distributed. The historical average temperature in Minnesota in December is ? = ?12.5 and standard deviation ? = 6. Use Table 1.

Calculate the expected temperature value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard error" to 4 decimal places.)

What is the probability that the sample mean temperature is less than ?13? (Round final answer to 4 decimal places.)

What is the probability that the sample mean temperature falls between ?13 and ?12? (Do not round intermediate calculations; round final answer to 4 decimal places.)

A random sample of air temperatures in December is taken from n = 66cities in Minnesota. Temperature data is known to be normally distributed. The historical average temperature in Minnesota in December is ? = ?12.5 and standard deviation ? = 6. Use Table 1.

Explanation / Answer

Solution:- Given that ? = ?12.5 and standard deviation ? = 6, n = 66

a.  Expected value = ?12.5

    Standard error = 6/sqrt(66) = 0.7385

b. P(X < -13) = P(Z < (-13 + 12.5)/(6/sqrt(66))

= P(Z < -0.677)

= 0.2483

c. P(-13 < X < -12) = P((-13 + 12.5)/(6/sqrt(66) < Z < (-12 + 12.5)/(6/sqrt(66))

= P(-0.677 < Z < 0.677)

= 0.5034

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