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Ugo [173]
3 years ago
6

According to a certain website, wine critics generally use a wine-scoring scale to communicate their opinions on the relative qu

ality of wines. Wine scores range from 0 to 100, with a score of 95–100 indicating a great wine, 90–94 indicating an outstanding wine, 85–89 indicating a very good wine, 80–84 indicating a good wine, 75–79 indicating a mediocre wine, and below 75 indicating that the wine is not recommended. Random ratings of a pinot noir recently produced by a newly established vineyard in 2018 follow:
87 91 86 82 72 91
60 77 80 79 83 96

Required:
a. Develop a point estimate of mean wine score for this pinot noir.
b. Develop a point estimate of the standard deviation for wine scores received by this pinot noir. (Round your answer to four decimal places.)
Mathematics
1 answer:
const2013 [10]3 years ago
3 0

Answer:

\bar x = 82

\sigma =  9.64

Step-by-step explanation:

Given

n = 12

87\ 91\ 86\ 82\ 72\ 91\ 60\ 77\ 80\ 79\ 83\ 96

Solving (a); Point estimate of mean

To do this, we simply calculate the sample mean

\bar x = \frac{\sum x}{n}

\bar x = \frac{87+ 91+ 86+ 82+72+91+60+77+80+79+83+96}{12}

\bar x = \frac{984}{12}

\bar x = 82

Solving (b); Point estimate of standard deviation

To do this, we simply calculate the sample standard deviation

\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n - 1}

\sigma = \sqrt\frac{(87-82)^2+ (91-82)^2+ ....+ (79-82)^2+ (83-82)^2+ (96-82)^2}{12-1}

\sigma = \sqrt\frac{1022}{11}

\sigma = \sqrt{92.91}

\sigma =  9.64

<em>Note that: The sample mean and the sample standard deviation are the best point estimators for the mean and the standard deviation, respectively.</em>

<em>Hence, the need to solve for sample mean and sample standard deviation</em>

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