Download Mod 17 Normal Distribution ACT1

Module 17 Normal Distribution Activity (1)
Use Statcrunch for normal distributions to answer the following probabilities. Write all answers with a
sentence in context. For Statcrunch go to: Stat-Calculators-Normal. Enter the mean and standard
deviation. Then choose the correct inequality and compute.
1. The mean height for males in the U.S. is 69 inches (𝜇 = 69) with a standard deviation of 3 inches
(𝜎 = 3).
a. Draw a diagram of the normal distribution showing the 68-95-99.7 tick marks for the height of males.
Then verify your cutoffs with Statcrunch.
b. A typical male height is between ______ and _______ inches.
c. An unusual male height is below ________ inches and above _______ inches.
d. An extremely unusual male height is above ________ inches and below ________ inches.
Using Statcrunch (and write your answer in a complete sentence):
e. P( x > 70)
f. P( x > 68)
g. P( x < 71)
h. P( x < 67)
i. P( 68 < x < 70)
2. Bald eagles mean wingspan is 6.7 feet (𝜇 = 6.7) with a standard deviation of 0.8 feet (𝜎 = 0.8).
a. Draw a diagram of the normal distribution showing the 68-95-99.7 tick marks for the wingspan of bald
eagles. Then verify your cutoffs with Statcrunch.
b. A typical wingspan is between ______ and _______ feet.
c. An unusual wingspan is below ________ feet and above _______ feet.
d. An extremely unusual wingspan is above ________ feet and below ________ feet.
Using Statcrunch (and write your answer in a complete sentence):
e. P( x < 6.9)
f. P( x < 6.0)
g. P( x >7.0)
h. P( x > 6.5)
i. P( 6.4 < x < 6.8)
3. The birth weights of full-term babies are normally distributed with a mean weight of μ =3400 grams and a
standard deviation of σ=505 grams.
a. Draw a diagram of the normal distribution showing the 68-95-99.7 tick marks for the birth weights of
babies. Then verify your cutoffs with Statcrunch.
b. A typical birth weight is between ______ and _______ grams.
c. An unusual birth weight is below ________ grams and above _______ grams.
d. An extremely unusual birth weight is above ________ grams and below ________ grams.
Using Statcrunch (and write your answer in a complete sentence):
e. P( x > 3500)
f. P( x > 3300)
g. P( x < 3600)
h. P( x < 3100)
i. P( 3350 < x < 3550)
4. The lengths of human pregnancies are normally distributed with a mean length of μ = 266 days and a
standard deviation of σ = 16 days.
a. Draw a diagram of the normal distribution showing the 68-95-99.7 tick marks for the lengths of
human pregnancies. Then verify your cutoffs with Statcrunch.
b. A typical pregnancy lasts between ______ and _______ days.
c. An unusual pregnancy lasts below ________ days and above _______ days.
d. An extremely unusual pregnancy lasts above ________ days and below ________ days.
Using Statcrunch (and write your answer in a complete sentence):
e. P( x < 287)
f. P( x < 255)
g. P( x >270)
h. P( x > 260)
i. P( 250 < x < 275)