Heights ofmale studentsare normally distributed with a mean of 175cm and a stand

Question

Heights ofmale studentsare normally distributed with a mean of 175cm and a standarddeviation of 8cnl.
i) What percentage of male students will have heights less than160cm?
ii) What percentage of male students will have heights between160cm and 170cm?
iii) Find the 90th percentile ofthis height distribution.
iv) Suppose 64 male students are randomly chosen from thispopulation.
Find the probability that the average height in this sample is morethan 173cm. Heights ofmale studentsare normally distributed with a mean of 175cm and a standarddeviation of 8cnl.
i) What percentage of male students will have heights less than160cm?
ii) What percentage of male students will have heights between160cm and 170cm?
iii) Find the 90th percentile ofthis height distribution.
iv) Suppose 64 male students are randomly chosen from thispopulation.
Find the probability that the average height in this sample is morethan 173cm.

Explanation / Answer

Given =175, s=8

(i) P(X<160)
=P((X-)/s < (160-175)/8)
=P(Z<-1.88)
=0.03 (check normal table) (iii) P(X<c) = 0.9
--> P((X-)/s < (c-175)/8) = 0.9
--> P(Z<(c-175)/8) =0.9
--> (c-175)/8 = 1.282 (check normal table)
--> c= 175 + 8*1.282 =185.256
(iv) P(Xbar>173)
=P((Xbar-)/(s/n) > (173-175)/(8/sqrt(64)))
=P(Z>-2)
= 0.9772 (check normal table)

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