Question

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SHOW WORK!!!!! Full credit will not be given for answers only. NOTE: for any question asking you to determine a probability----you MUST write out a probability statement using proper notation!!!! Probabilities should be DECIMAL form and rounded to 4 decimal places.

Jack is a collegiate high jumper. The heights of his jumps follow a normal distribution with an average of 6 feet 3 inches with a standard deviation of 8 inches. Let Y be the height of one of Jack’s jump. (Note: high jumpers try to jump over a bar that is set at a particular height for an attempt. Clearing the bar means that the high jumper went over the bar w/o knocking it down.)

a) The bar is currently set at 7 feet 3 inches. What is the probability that Jack does not clear the bar?
b) What is the probability that Jack jumps at least 8 feet in his attempt?
c) What is the probability that Jack’s attempt is within 5 inches of his average?
d) What is the 90th percentile of Jack’s jump heights?
e) Jack has already done a few jumps in a competition and is very tired. He knows that on his next jump he can only jump at most 7 feet. If the bar is set at 6.17 feet, what is the probability that he clears it?

Answer 1

Y is the random variable denoting the height jumped by Jack in inches .

Note that 6 feet 3 inches = 75 inches

So, Y~N( 75 , 8)

a) P[ Jack does not clear the bar]

b) P[ Jack attempts at least 8 ft]

c) Jacks average is 75 inches .

So we need to find :

d) Let p be the 90th percentile ,

Then by definition of percentile :

inches or 7.105 ft.

e) 6.17 ft = 6.17 x 12 inches = 74.04 inches .

We need to find :

* where Z~N(0,1)