Download Quiz 4 Math 220 1. It is reasonable to assume the heights of male

Quiz 4 Math 220
1. It is reasonable to assume the heights of male college students are
normally distributed. It is known the mean height is 70 inches with standard
deviation 2.8 inches.
1). You choose a student at random. What is the probability he is taller
than 71 inches?
) = P (z > 0.36) = 1 − 0.6406 = 0.3594.
P (x > 71) = P (z > 71−70
2.8
2). You choose a SRS of 25 students. What is the probability the mean
height of your sample is bigger than 71 inches?
Note σx̄ = √2.8
= 0.56.
25
P (x̄ > 71) = P (z > 71−70
) = P (z > 1.79) = 1 − P (z ≤ 1.79) =
0.56
1 − 0.9633 = 0.0367.
2. A manager in a baby food factory suspects the containers of the baby
food in his factory are underfilled. The average net weight of 16 containers
he randomly took is 497.5 grams. Suppose the net weights of the containers
follow a normal distribution with a known standard deviation σ = 3 grams.
1). Get a 95% confidence interval for µ, the mean weight of baby food
containers in the factory. What is the margin of error of your confidence
interval?
x̄ ± z0.025 √σn = 497.5 ± 1.96 √316 = (496.03, 498.97) grams.
The margin of error is 1.96 ∗ √316 = 1.47.
2). Suppose it is desired the margin of error of the 95% CI is 1 gram.
What sample size is needed to achieve this?
Set 1.96 ∗ √3n = 1, we get n ≈ 35.
or n = ( 1.96∗3
)2 ≈ 35.
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