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## Homework Statement

3 (a) A sample of 50 washed baking potatoes was selected at random from a large batch.

The weights of the 50 potatoes were found to have a mean of 234 grams and a standard

deviation of 25.1 grams.

Construct a 95% confidence interval for the mean weight of potatoes in the batch.

(4 marks)

3 (a) A sample of 50 washed baking potatoes was selected at random from a large batch.

The weights of the 50 potatoes were found to have a mean of 234 grams and a standard

deviation of 25.1 grams.

Construct a 95% confidence interval for the mean weight of potatoes in the batch.

(4 marks)

## Homework Equations

[itex] \bar{x} = \mu[/itex]

[itex] s = \frac{\sigma}{\sqrt{n}}[/itex]

[itex] z = \frac{x-\mu}{s}[/itex]

## The Attempt at a Solution

The confidence interval 95% means p = 0.975

[itex] z = \frac{x-\mu}{s}[/itex]

[itex] \pm 1.96 = \frac{x-234}{\frac{25.1}{\sqrt{50}}}[/itex]

[itex]\Rightarrow 227-241[/itex]

Why is the standard deviation

[itex]s = \frac{25.1}{\sqrt{50}}[/itex]

and not just 25.1. The question states that the s.d. is 25.1!