Respuesta :
Answer:
[tex]\mu = 55[/tex]
[tex]\sigma = 6[/tex]
(a) What is the probability that a randomly chosen 10 year old is shorter than 51 inches?
Formula : [tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{51-55}{6}[/tex]
[tex]z=−0.666[/tex]
refer the z table
P(z<-0.66)=0.2546
Hence the probability that a randomly chosen 10 year old is shorter than 51 inches is 0.2546
(b) What is the probability that a randomly chosen 10 year old is between 57 and 67 inches?
Formula : [tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{57-55}{6}[/tex]
[tex]z=0.333[/tex]
refer the z table
P(z<0.333)=0.6293
[tex]z=\frac{67-55}{6}[/tex]
[tex]z=2[/tex]
refer the z table
P(z<2)=0.9772
P(57<x<67)=P(0.333<z<2)=P(z<2)-P(z<0.333)= 0.9772-0.6293=0.3479
Hence the probability that a randomly chosen 10 year old is between 57 and 67 inches is 0.3479
c) If the tallest 10% of the class is considered "very tall", what is the height cutoff for "very tall"?
1 - 0.10 = 0.9
Refer the z table
probability of shortest = 0.98
z corresponding 0.9 = 1.28
[tex]1.28=\frac{x-55}{6}[/tex]
[tex]7.68=x-55[/tex]
[tex]7.68+55=x[/tex]
[tex]62.68=x[/tex]
Hence the height cutoff for "very tall" is 62.98
d)The height requirement for Batman the Ride at Six Flags Magic Mountain is 54 inches. What percent of 10 year olds cannot go on this ride?
[tex]z=\frac{54-55}{6}[/tex]
[tex]z=−0.166[/tex]
p(z<-0.166)=0.4364
Hence 43.64% of 10 year olds cannot go on this ride
