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.