Question

The set numbers are  normally distributed with μ = 100 and σ = 15; X ~ N(100, 10)

Solution

68% of scores within μ ± σ

= 100 ± 15

= 85 to 115

95% of scores within μ ± 2σ

= 100 ± (2)(15)

= 70 to 130

99.7% of scores in μ ± 3σ =

100 ± (3)(15)

= 55 to 145

Question

The average female height in the United States is 63 inches, having the standard deviation of 2.4.

Solution

We’ll represent this as

68% is within  μ ± σ: 63 ± 2.4= 60.6 to 65.4

32% is in the tails (below 60.5 and above 65.4)

16% is below 60.6 and 16% is above 65.4

Question

The average household income for people who can afford to buy a single family    home in California is $120k.The standard deviation is $17k. 30% of families weren’t able to afford a single family home. What is the minimum income required to buy a single family home in California?

Solution

Question

The goods carrier tuck travels an average speed of 50 miles/hr  and a standard deviation of 15 mile/hr. Truck company wants to know the probability of trucks that will have speed between  50 and 70 miles/hours.

Solution

Let x be the random variable that represents the speed. It has a mean of 50 miles/hr  and a standard deviation of 15 miles/hr. We have to find the probability that x is between 50 and 70 or P( 50< x < 70)

For x = 50 , z = (50 - 50) / 15 = 0

For x = 70 , z = (70 - 50) / 15 = 1.33 P( 50< x < 70) = P( 0< z < 1.33) = [area to the left of z = 1.33] - [area to the left of z = 0]=

0.9082 - 0.5 = 0.4082

The probability of a truck that has a speed between 50 and 70 miles/hours is equal to 0.4082.