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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

The increased number of small commuter planes in major airports has heightened concern over air safety. An eastern airport has recorded a monthly average of nine near misses on landings and takeoffs in the past 5 years. (Round your answers to three decimal places.)

(a) Find the probability that during a given month there are no near misses on landings and takeoffs at the airport . 

(b) Find the probability that during a given month there are three near misses.

(c) Find the probability that there are at least three near misses during a particular month.