Question

Applying the Concepts NW 31. You Explain It! Cell Phone Rates Monthly charges for cell phone plans in the United States are normally distributed with mean μ $62 and standard deviation σ $18. Source: Based on information from Consumer Reports

Answer 1

Answer

(A) Use mean = 62 and standard deviation = 18 to draw the curve  

mean will be the center for normal curve

$\mu \pm \sigma = 62 \pm 18 = (44,80)$

$\mu \pm 2\sigma = 62 \pm 2*18 = (26,98)$

$\mu \pm 3\sigma = 62 \pm 3*18 = (8,116)$

Drawing 8,26 and 44 on the left side of mean and 80,98,116 on the right hand side of mean

(B) To shade the area below 44, shade all the region below 44 till the left end by dark color

we get

26 62 80 98 116

(C) area to the left of 44 is 0.1587, this means that there is 0.1587 probability of finding a monthly charge for cell phone below $44.

total probability is always 1, so we can say that 1-0.1587 = 0.8413

This means that x = $44, tells us that there is 0.8413 probability of finding a monthly charge for cell phone above $44.