Adrian has a bag full of pebbles that all look about the same. he weighs some of the pebbles and finds that their weights are normally distributed, with a mean of 2.6 grams and a standard deviation of 0.4 grams. what percentage of the pebbles weigh more than 2.1 grams? round to the nearest whole percent.

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tutorconsortium201 tutorconsortium201 · Answer 1 · 2022-08-10T12:44:13+02:00

89% of pebbles weigh more than 2.1 grams.

What is a percentage?

Percentage, a relative value indicating hundredth parts of any quantity.
One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.

Given,

Mean = 2.6

SD = 0.4

As we have to find the percentage of pebbles weighing more than 2.1, we have to find the z-score for 2.1 first.

[tex]z = \frac{x- mean}{SD}[/tex]

[tex]z = \frac{2.1 - 2.6}{0.4}[/tex]

[tex]z = -1.25[/tex]

Now we have to use the z-score table to find the percentage of pebbles weighing less than 2.1

So,

[tex]P ( x < 1.25 ) = 0.10565[/tex]

This gives us the probability of P(z<-1.25) or P(x<2.1)

To find the probability of pebbles weighing more than 2.1

[tex]P ( x > 2.1 ) = 1 - P( x < 2.1 ) = 1 - 0.10565 = 0.89435[/tex]

Converting into percentage

0.89435 × 100 = 89.435 %

Rounding off to nearest percent =89%

Therefore, 89% of pebbles weigh more than 2.1 grams.

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