Explain why the t-distribution has less spread as the number of degrees of freedom increases.

(a) the t-distribution has less spread as the degrees of freedom increase because, for large values of n, ngreater than or equals30, the t-distribution and the normal distribution are the same.

(b) the t-distribution has less spread as the degrees of freedom increase because, as n increases, less information is known about sigma by the law of large numbers.

(c) the t-distribution has less spread as the degrees of freedom increase because the variability introduced into the t-statistic becomes greater as n increases.

(d) the t-distribution has less spread as the degrees of freedom increase because, as n increases, s becomes closer to sigma by the law of large numbers.

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A Carnot heat engine receives heat from a reservoir at 900$^\circ{}$C at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 27$^\circ{}$C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at -5$^\circ{}$C and transfers it to the same ambient air at 27$^\circ{}$C. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air. Answers: (a) 4982 kJ/min, (b) 5782 kJ/min

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