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Chapter 5: Q39E (page 320)

A random sample of n = 250 measurements is drawn from a binomial population with a probability of success of .85.

  1. FindEP⏞andσp⏞
  2. Describe the shape of the sampling distribution ofp⏜.
  3. Find

Short Answer

Expert verified

Random sampling is a sample strategy in which every sample has an equal probability of being selected. A random sample is intended to provide an impartial reflection of the overall population.

Step by step solution

01

 Step 1: (a) The data is given below

The calculation is given below:

Given,

p=0.85Population Proportion= 1-P=1-0.85=0.15

n=250Sample Size

The sample proportionis p⏜.

Mean =μp⏞P=0.85

SDσp⏜=p1-p/ n=0.85×0.15250=0.02258317

μp⏜=0.85σp⏜=0.02258317

02

(b) The data is given below

The calculation is given below:

Since bothn×p and n×1-pare>=10, so

The p⏜sampling distribution is about normal.

03

(c) The data is given below

The calculation is given below:

pp⏜-μp⏜/σp⏜<0.9-μp⏜/μp⏜=PZ<0.9-0.85/0.02258317=PZ<2.21=0.9864...use z table

pp⏜<0.9=0.9864

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Most popular questions from this chapter

A random sample of n = 80 measurements is drawn from a binomial population with a probability of success .3.

  1. Give the mean and standard deviation of the sampling distribution of the sample proportion, p¯
  2. Describe the shape of the sampling distribution of p¯
  3. Calculate the standard normal z-score corresponding to a value of p¯=0.35
  4. FindP(p)¯=0.35

A random sample of n= 300 observations is selectedfrom a binomial population with p= .8. Approximateeach of the following probabilities:

  1. Pp^<0.83
  2. Pp^>0.75
  3. P0.79<p^<0.81

Tomato as a taste modifier. Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste. Refer to the Plant Science (May 2010) investigation of the ability of a hybrid tomato plant to produce miraculin, Exercise 4.99 (p. 263). Recall that the amount x of miraculin produced in the plant had a mean of 105.3 micrograms per gram of fresh weight with a standard deviation of 8.0. Consider a random sample of n=64hybrid tomato plants and letx represent the sample mean amount of miraculin produced. Would you expect to observe a value of X less than 103 micrograms per gram of fresh weight? Explain.

:A random sample of n = 68 observations is selected from a population withμ=19.6and σ=3.2Approximate each of the following probabilities

a)pX¯⩽19.6

b)pX¯⩽19

c)pX¯⩾20.1

d)p19.2⩽X¯⩽20.6

Question: Refer to Exercise 5.3.

  1. Show thatxis an unbiased estimator ofμ.
  2. Findσx2.
  3. Find the x probability that x will fall within2σxofμ.
See all solutions

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