1.A population has a mean of 400 and a standard deviation of 90. Suppose a sampl

Question

1.A population has a mean of 400 and a standard deviation of 90. Suppose a sample of size 100 is selected and  (x-bar) is used to estimate  (mu).

A.What is the probability that the sample mean will be within +/- 8 of the population mean (to 4 decimals)?

B.What is the probability that the sample mean will be within +/- 16 of the population mean (to 4 decimals)?

2.The Democrat and Chronicle reported that 25% of the flights arriving at the San Diego airport during the first five months of 2001 were late (Democrat and Chronicle, July 23, 2001). Assume the population proportion is p = .25.

A.Calculate () (sigma p-bar) with a sample size of 1,200 flights (to 4 decimals).

B.What is the probability that the sample proportion lie between 0.22 and 0.28 if a sample of size 1,200 is selected (to 4 decimals)?

C. What is the probability that the sample proportion will lie between 0.22 and 0.28 if a sample of size 600 is selected (to 4 decimals)?

3.A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400 = .375?

A.Calculate the probability to 4 decimals.

Explanation / Answer

Since it has 3 different questions I and it is not sated whiich wuestion to answer as per chegg policy I answer the first question with its 2 sub parts:

1. X(mean)tends to normal(sample mean, sd^2/no. of observation)

this implies X(mean) tends to normal(400,36)

P(392<X(mean)<408)

=P((392-400)/6<Z<(408-400)/6).............(where Z refers to standared normal distribution)

=P(-1.3333<Z<1.3333)

Since Z(1.33)=.90824

So, given probability is 2(.90824-.5)=0.8165

Simmilarly upto +/-16

P(-2.66<Z<2.66)=2*(.99609 -0.5)

=099218

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.