Question

**Show all of your work!**

2. The president of Doerman Distributors, Inc.
believes that 30% of the firm’s orders come from new or first-time
customers. A simple random sample of 100 orders is used to estimate
the proportion of new or first-time customers. The results of the
sample will be used to verify the president’s claim of *p* =
0.30.

a. Show whether the study meets the success/failure condition. (1 point)

b. What is the probability that the sample proportion is less than 0.20 [P(z ≤ 0.20)? (1 point)

c. What is the probability that the sample proportion is less than 0.40 [P(z ≤ 0.40)? (1 point)

d. What is the probability that the sample proportion will be between 0.20 and 0.40 [P(0.20 ≤ ≤ 0.40)]? (1 point)

Answer #1

a)

Success / failure conditions are

np = 100 * 0.30 = 30 >= 10 ---> holds.

nq = 100 * (1-0.30) = 70 >= 10 ----> holds.

The study meets success / failure conditions.

b)

Using central limit theorem,

P( < p ) = P( Z < - p / sqrt( p( 1 - p) / n) )

P( < 0.30 ) = P( Z < 0.20 - 0.30 / sqrt( 0.30 * 0.70 / 100) )

= P( Z < -2.1822)

= **0.0145**

b)

P( < 0.40) = P( Z < 0.40 - 0.30 / sqrt( 0.30 * 0.70 / 100) )

= P( Z < 2.1822)

= **0.9855**

c)

P( 0.20 <= <= 0.40) = P( <= 0.40) - P( <= 0.20)

= P( Z < 0.40 - 0.30 / sqrt( 0.30 * 0.70 / 100) ) + P( Z < 0.20 - 0.30 / sqrt( 0.30 * 0.70 / 100) )

= P( Z < 2.1822) - P( Z < -2.1822)

= **0.9710**

The president of Doerman Distributors, Inc., believes that 30%
of the firm's orders come from first-time customers. A random
sample of 150 orders will be used to estimate the proportion of
first-time customers.
(a)Assume that the president is correct and p
= 0.30.
What is the sampling distribution of p for n =
150? (Round your answer for σp to four
decimal places.)
σp=
E(p)=
Since np = and n(1 − p)
= , approximating the sampling distribution with a
normal distribution ---Select---...

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The president of Doerman Distributors, Inc., believes that 26%
of the firm's orders come from first-time customers. A simple
random sample of 100 orders will be used to estimate the proportion
of first-time customers. Use z-table.
Assume that the president is correct and p = 0.26.
What is the sampling distribution of for this
study?
SelectA normal distribution because np and n(1-p) are both greater
than 5A normal distribution because np and n(1-p) are both...

Based on historical data, your manager believes that 27% of the
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Based on historical data, your manager believes that 33% of the
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Answer should be 4 decimal places.

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Note: You should carefully round any z-values you calculate to 4
decimal places to match wamap's approach and calculations.
Answer = (Enter your answer as a number accurate to 4
decimal places.)

Based on historical data, your manager believes that 32% of the
company's orders come from first-time customers. A random sample of
178 orders will be used to estimate the proportion of
first-time-customers. What is the probability that the sample
proportion is less than 0.29?
Note: You should carefully round any z-values you calculate to 4
decimal places to match wamap's approach and calculations.
Answer = (Enter your answer as a number accurate to 4
decimal places.)

Based on historical data, your manager believes that 28% of the
company's orders come from first-time customers. A random sample of
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