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Vesna [10]
3 years ago
5

1a. [1 mark] The price per kilogram of tomatoes, in euros, sold in various markets in a city is found to be normally distributed

with a mean of 3.22 and a standard deviation of 0.84. Find the price that is two standard deviations above the mean price.
Mathematics
1 answer:
andrey2020 [161]3 years ago
3 0

Answer:

The price that is two standard deviations above the mean price is 4.90.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 3.22 and a standard deviation of 0.84.

This means that \mu = 3.22, \sigma = 0.84

Find the price that is two standard deviations above the mean price.

This is X when Z = 2. So

Z = \frac{X - \mu}{\sigma}

2 = \frac{X - 3.22}{0.84}

X - 3.22 = 2*0.84

X = 4.9

The price that is two standard deviations above the mean price is 4.90.

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