Respuesta :
Answer:
B. About 2% of the boys are eligible to be a small forward on the team
Step-by-step explanation:
Recall : 1 feets = 12 inches
Point guard = 6’2" – 6’6" tall = 74 - 78 inches
Mean = 70 ; Standard deviation = 4
Z = (x - mean) / standard
P(x < 74) = (74 - 70) / 4 = 1
P(x < 78) = (78 - 70) / 4 = 2
0.97725 - 0.84134 = 0.13591
Small forward : 6'6" = 78 inches
P(x ≥ 78) = (78 - 70) / 4 = 2
P(z ≥ 2) = 0.02275 = 2.275% about 2%
Centre : 6'8" = 80
P(x ≥ 80) = (80 - 70) / 4 = 2.5
P(z ≥ 2.5) = 0.0062097 = 0.62%
About 2% of the boys are eligible to be a small forward on the team. Then the correct option is B.
What is a z-score?
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
A high school basketball coach is selecting his team.
The minimum and maximum height requirements are as follows:
Point Guard: Small Forward: Center:
6’2" – 6’6" tall at least 6’6" tall at least 6’8" tall
The heights of the Lincoln High School boys have a normal distribution with a mean height of 70 inches and a standard deviation of 4 inches.
The value of the z-score will be
[tex]z = \dfrac{x - \mu }{\sigma}[/tex]
[tex]P(x < 74) = \dfrac{74-70}{4} = 1 \\\\P(x < 78) = \dfrac{78-70}{4} = 2[/tex]
0.97725 - 0.84134 = 0.13591
Small forward: 6'6" = 78 inches
[tex]P(x \geq 78) = \dfrac{78- 70 }{4} 2\\\\\\P(z \geq 2) = 0.02275 = 2.275 \%[/tex]
Centre: 6'8" = 80 inches
[tex]P(x \geq 80) = \dfrac{80- 70 }{4} 2\\\\\\P(z \geq 2.5) = 0.0062097= 0.62 \%[/tex]
More about the z-score link is given below.
https://brainly.com/question/13299273
