Question

A normal distribution of values has a mean of 47 and a standard deviation of 3.2. Which of the numbered choices is the percentage of values that lie between 42 and 50?

1) 17.4% 2) 59.1% 3) 76.7% 4) 82.4%

Answer 1

Given:
μ = 47, population mean
σ = 3.2, population standard deviation

When the random variable is x = 42, the -score is
z = (42 - 47)/3.2 = -1.5625
From normal tables, the area to the left of is
0.0591 = 5.91%

When x = 50,
z = (50 - 47)/3.2 = 0.9375
The area to the left of z is
0.8257 = 82.57%

Therefore the area between x= 42 and x=50 is
82.57 - 5.91 = 76.66%

Answer: 3)
The correct answer is 76.7%