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 the standard deviation of 4 inches.

Which statement is true?

A. About 16% of the boys are eligible to be a point guard on the team. B. About 2% of the boys are eligible to be a small forward on the team. C. About 48% of the boys are eligible to be a small forward on the team. D. About 34% of the boys are eligible to be a point guard on the team.

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%

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47