Provide an appropriate response.Assume that the heights of men are normally distributed with a mean of 68.5 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height greater than 69.5 inches.

Provide an appropriate response.A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize the boys whose times are among the top (or fastest) 10% with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?

Find the indicated probability.Assume that the random variable X is normally distributed, with mean and standard deviation Compute the probability P(X < 105).

Find the indicated probability.Assume that the random variable X is normally distributed, with mean and standard deviation Compute the probability P(X > 126).

In local regression, the estimated function at a point x0x_0​ is typically written as

A basis function used in a piecewise cubic spline with a knot at cc is:

What does a knot represent in the context of splines?

In the context of local regression, what does the term ‘weighted least squares’ refer to?

What role does the smoothing parameter λ play in smoothing splines?

The penalty term λ∫[f′′(t)]2dt\lambda \int [f”(t)]^2 dt in a smoothing spline controls