Normal Distribution

Given z-score

100

p(z < -2.05)

.0202 or 2.02%

200

p(z < 1.36)

.9131 or 91.31%

300

p(z < 5.16)

1 or 100%

400

p(-2 < z < 1)

.8185 or 81.85%

500

p( 1.14 < z < 2.49)

.1207 or 12.07%

Just the info

100

Mean = 23 and standard deviation is 1.5 p(x > 20)

.9772 or 97.72%

200

Mean = 40 and standard deviation is 13 p(z < 16)

.0322 or 3.22%

300

Mean = 40 and standard deviation is .8 p(x < 41)

.1056 or 10.56%

400

Mean = 60 and standard deviation = 10 p(30 < x < 70)

.84 and 84%

500

Mean = 40 and standard deviation = 7 p(35 < x < 60)

.7539 or 75.39%

Word Problems

100

The average amount of hot fries in a bag is 8.5 ounces with a standard deviation of .5 ounces. What percent of bags have more than less than 7 ounces?

.0013

200

Cookie man cookies have a diameter of 2.5 inches with a standard deviation of .15 inches. What percent of cookies have a diameter of more than 3 ounces

.0004 or .04%

300

The average baby is born weighing 7.8 pounds with a standard deviation of 1 pound. What percent of babies weigh more than 11 pounds?

.07%

400

Water bottles are supposed to hold 12 ounces with a standard deviation of .2 ounces. What percent of the water bottles hold between 12 and 12.6 ounces

49.87%

500

The average male is 72 inches tall (6 feet) with a standard deviation of 3.5 inches. What percent of men are over 7 feet tall?

.03%

Binomial approximation

100

Find P(X=3) using the formula for P(X=k) for a Binomial Distribution, given that n=56 and p=0.12.

(normal approximation to the binomial distribution)

0.055

200

Given that n=6 and p=0.76, find P(X≥4)

(normal approximation to the binomial distribution)

0.846

300

Suppose that 15% of students at ECHS play sports. If there are 32 students in 1st period, what is the probability that 4 students in 1st period play sports?

(this is binomial probability)

0.19

400

Suppose we throw the single die 5 times. What is the probability that the die lands on "2" three times?

(binomial probability)

0.032

500

Using the fact that 12% of people wear contact lenses. If ECHS had 1075 students, what would be the probability that at least 151 students wear contact lenses?

(normal approximation to the binomial distribution)

0.025