Find probability’

Question

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 13 minutes. Consider 49 of the races.

Let X

 = the average of the 49 races.

Find the probability that the average of the sample will be between 144 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.)

Answer 1

µ=145

σ=13

n=49

Since n is large, according to the central limit theorem, the sampling distribution of X is approximately normal. If you are using a TI84

P(144 < X < 148) = normalcdf(144,148,145,13/sqrt(49)) = 0.6518

or

P(144 < X < 148) = P((144-145)/(13/sqrt(49) < Z < (148-145)/(13/sqrt(49))

P(-0.5385 < Z < 1.6154)

this can also be solved with a TI84

=normalcdf(-0.5385, 1.6154,0,1)=0.6518

or with tables.

If you want you can let me know what method you use in your class and I can explain it that way.

Let me know if you have any questions.

Dian