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Ksenya-84 [330]
2 years ago
10

Suppose the number of a particular type of bacteria in samples of 1 milliliter (ml) of drinking water tend to be approximately n

ormally distributed, with a mean of 85 and a standard deviation of 9. What is the probability that a given 1-ml will contain more than 100 bacteria
Mathematics
1 answer:
Irina-Kira [14]2 years ago
3 0

Answer: 0.0475

Step-by-step explanation:

Let x = random variable that represents the number of a particular type of bacteria in samples of 1 milliliter (ml) of drinking water, such that X is normally distributed.

Given: \mu=85,\ \ \sigma=9

The probability that a given 1-ml will contain more than 100 bacteria will be:

P(X>100)=P(\dfrac{X-\mu}{\sigma}>\dfrac{100-85}{9})\\\\=P(Z>1.67)\ \ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Zz)=1-P(Z

∴The probability that a given 1-ml will contain more than 100 bacteria

0.0475.

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