the heights of US male students in high school is normallydistributed with a mea
ID: 3096302 • Letter: T
Question
the heights of US male students in high school is normallydistributed with a mean of 67 inches with a standard deviation of 3inches.What is the probability that a student is either taller than70 inches or shorter than 61 inches?
What is the probability that a student is between 64 inchesand 73 inches?
If there are 250 males in high school, how many would youexpect to find taller than 73 inches?
If 100 male students are randomly chosen, how many would youexpect to be shorter than 64 inches?
Please show all work. Thanks.
What is the probability that a student is either taller than70 inches or shorter than 61 inches?
What is the probability that a student is between 64 inchesand 73 inches?
If there are 250 males in high school, how many would youexpect to find taller than 73 inches?
If 100 male students are randomly chosen, how many would youexpect to be shorter than 64 inches?
Please show all work. Thanks.
Explanation / Answer
What is the probability that a student is either taller than70 inches or shorter than 61 inches?P(X<61 or X>70) =P(X<61)+P(X>70)
=P((X-)/ < (61-67)/2) + P((X-)/> (70-67)/3 )
=P(Z<-3) + P(Z>1)
= 0.16 (check normal table)
What is the probability that a student is between 64 inchesand 73 inches?
P(64<X<73)= P((64-67)/3 <Z< (73-67)/3)
=P(-1<Z<2)
= 0.8186 (check normal table)
If there are 250 males in high school, how many would youexpect to find taller than 73 inches?
P(X>73)=P(Z>(73-67)/3)
=P(Z>2)
= 0.0227
250* 0.0227 = 5.675
If 100 male students are randomly chosen, how many would youexpect to be shorter than 64 inches? P(X<64)=P(Z<(64-67)/3)
=P(Z<-1)
= 0.1586
100* 0.1586 = 15.86
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