Ch.7+8 Continuous Prob. Distribution

Question 1

In Uniform Distribution, calculate
(between range a to b)

Mean
Variance
St. Deviation

Answer 1

μ = (a+b) / 2

. (b-a)²
σ² = ——–
. 12

σ = sqrt(σ²)

Question 2

In Normal Distribution,
calculate

x

Answer 2

x = μ + z·σ

Question 3

In Normal Distribution,
calculate
z for
1. Population
2. Sample
3. Proportion

Answer 3

1.. x-μ
z = ——-
. σ
=NORM.S.INV(prob.)
2.. x-μ
z = ————–
. σ / sqrt(n)
3.. phat-p
z = —————
. sqrt(p·q/n)

Question 4

When using
NORM.S.DIST(z,1)
in Excel,
the probability value
represents the area to the ____ under the bell-shape curve

Answer 4

LEFT

Question 5

In Normal Distribution,
Given x ₁ & x ₂,
Steps in Excel to find

P(x₁ < x < x₂)

Answer 5

1. Find z₁ & z₂ from
   z = (x-μ)/σ
   round 2-digit decimal
2. Find P(x<x₁) & P(x<x₂) from NORM.S.DIST(z,true)
3. P(x<x₂) - P(x<x₁)
   4-digit decimal

given x→ formula z→ excel prob

Question 6

In Normal Distribution,
Given Prob.1 & Prob.2,
Steps in Excel to find

Range of x₁ & x₂

Answer 6

1. Find z₁ & z₂ from
   NORM.S.INV(Prob)
   round 2-digit decimal
2. Find x₁ & x₂ from
   x = μ+z·σ

given prob→ excel z→ formula x

Question 7

Distinguish to calculate

x / xbar / phat

Answer 7

1. Sample n? No → x
   Yes → 2.
2. About
   xbar → xbar (n>30)
   or proportion → phat (np&nq>5)

Question 8

σxbar

Answer 8

= σ / sqrt(n)

Question 9

σphat

Answer 9

= sqrt(pq/n)

Question 10

Checking of Normal Approximation
for
1. Sample
2. Proportion

Answer 10

1. n ≥ 30
2. n·p ≥ 5 & n·q ≥ 5