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Marysya12 [62]
2 years ago
8

Laboratory tests show that the lives of

Mathematics
1 answer:
SIZIF [17.4K]2 years ago
6 0
<h3>Answer:  34%</h3>

This result is approximate.

=========================================================

Explanation:

mu = 750 = mean

sigma = 75 = standard deviation

The raw scores or x values are x = 750 and x = 825

Let's compute the z score for each x value

z = (x - mu)/sigma

z = (750 - 750)/75

z = 0

and

z = (x - mu)/sigma

z = (825 - 750)/75

z = 1

Therefore P(750 ≤ x ≤ 825) is equivalent to P(0 ≤ z ≤ 1) in this context.

Use a z score table to determine that

P(z ≤ 0) = 0.5

P(z ≤ 1) = 0.84314 approximately

So,

P(a ≤ z ≤ b) = P(z ≤ b) - P(z ≤ a)

P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0)

P(0 ≤ z ≤ 1) = 0.84314 - 0.5

P(0 ≤ z ≤ 1) = 0.34314 approximately

The value 0.34314 then converts to 34.314% which rounds to <u>34%</u>

Or you could use the empirical rule as shown below. The pink section on the right is marked <u>34%</u> which is approximate. This pink section is between z = 0 and z = 1.

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