A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain supermarket. Each shopper was asked whether they had bought any wine in each of the last 4 weeks. Let x denote the number of weeks when a shopper bought wine and fdenote the number of shoppers who bought wine in x weeks. If a shopper had not bought any wine then x was set to zero. Results are given in the first two rows of the following table. Note that f- 34 shoppers did not buy any wine, f- 40 shoppers bought wine only in 1 of those 4 weeks and so on. 2 3 Total 34 40 64 56 200 Pi 0.0915 0.2995 0.3675 0.2005 0.0410 1 It has been suggested that these data are binomially distributed with n = 4 and some (unknown) parameter p, which is the probability that a randomly selected shopper will buy wine in any given week. Answer the following questions. a. Calculate the sample mean and the sample variance for these data. b. Estimate the parameter p for the suggested binomial distribution. c. Write down the formula to calculate the binomial probability P( X - 3) - 0.2005 (4dp), as given in the table. Show clearly how to use the answer from part (b) to calculate the probability given here. d. Use the p;values given in the table, which were obtained as in part (c), to calculate corresponding expected values, e; Give your expected values to 1 decimal place.
A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain supermarket. Each shopper was asked whether they had bought any wine in each of the last 4 weeks. Let x denote the number of weeks when a shopper bought wine and fdenote the number of shoppers who bought wine in x weeks. If a shopper had not bought any wine then x was set to zero. Results are given in the first two rows of the following table. Note that f- 34 shoppers did not buy any wine, f- 40 shoppers bought wine only in 1 of those 4 weeks and so on. 2 3 Total 34 40 64 56 200 Pi 0.0915 0.2995 0.3675 0.2005 0.0410 1 It has been suggested that these data are binomially distributed with n = 4 and some (unknown) parameter p, which is the probability that a randomly selected shopper will buy wine in any given week. Answer the following questions. a. Calculate the sample mean and the sample variance for these data. b. Estimate the parameter p for the suggested binomial distribution. c. Write down the formula to calculate the binomial probability P( X - 3) - 0.2005 (4dp), as given in the table. Show clearly how to use the answer from part (b) to calculate the probability given here. d. Use the p;values given in the table, which were obtained as in part (c), to calculate corresponding expected values, e; Give your expected values to 1 decimal place.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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a, b c and d please thank you
Transcribed Image Text:A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain supermarket.
Each shopper was asked whether they had bought any wine in each of the last 4 weeks.
Let x denote the number of weeks when a shopper bought wine and fdenote the number of shoppers who
bought wine in x weeks. If a shopper had not bought any wine then x was set to zero. Results are given in the first
two rows of the following table. Note that f = 34 shoppers did not buy any wine, f = 40 shoppers bought wine
only in 1 of those 4 weeks and so on.
1
2
3
14
Total
34
40
64
56
6
200
Pi
0.0915
0.2995
0.3675
0.2005
0.0410
1
It has been suggested that these data are binomially distributed with n = 4 and some (unknown) parameter
p, which is the probability that a randomly selected shopper will buy wine in any given week.
Answer the following questions.
a. Calculate the sample mean and the sample variance for these data.
b. Estimate the parameter p for the suggested binomial distribution.
c. Write down the formula to calculate the binomial probability P( X = 3) = 0.2005 (4dp), as given in
the table. Show clearly how to use the answer from part (b) to calculate the probability given here.
d. Use the p;values given in the table, which were obtained as in part (C), to calculate corresponding
expected values, ej. Give your expected values to 1 decimal place.
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