According to a study conducted by a university, children who are injured seven or more times tend to sustain these injuries during a relatively limited time, usually 1 year or less. Let the average number of injuries per year for school-age children be seven.

(a) Calculate the mean and standard deviation for x, the number of injuries per year sustained by a school-age child. (Round your answers to three decimal places.) 𝜇=  injuries 𝜎=  injuries

(b) According to Tchebysheff's Theorem, within what limits would you expect the number of injuries per year to fall at least three-quarters of the time? (Round your answer up to the nearest whole number.) 1  injury to   injuries

which of these neural injuries will the corneal reflex not test for?

Despite tuition skyrocketing, a college education is still valuable. Recent calculations by the Federal Reserve Bank in San Francisco demonstrate a college degree is worth $800,000 in lifetime earnings compared to the average high school education. Assume graduates in 2017 earn $40,132, $35,594, $42,392, $41,267, $55,600 and $51,368.

What is the variance for this sample? (Round your intermediate calculations and final answer to the nearest whole number.

What is the standard deviation for this sample? (Round your intermediate calculations and final answer to the nearest whole number.)

"Time headway" in traffic flow................

"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X=the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form.

(a) Determine the value of k for which f(x) is a legitimate pdf.

(b) Obtain the cumulative distribution function.

(c) Use the cdf from (b) to determine the probability that headway exceeds 2sec. (Round your answer to three decimal places).

(d) Obtain the mean value of headway and the standard deviation of headway.(Round your answers to three decimal places).

(e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answr to three decimal places).