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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.

Sagot :

absor201

Answer:

89% of pebbles weigh more than 2.1 grams.

Step-by-step explanation:

Given that

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}\\z = \frac{2.1-2.6}{0.4}\\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

[tex]0.89435*100 = 89.435\%[/tex]

Rounding off to nearest percent

89%

Hence,

89% of pebbles weigh more than 2.1 grams.

Answer:

89%

Step-by-step explanation:

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