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The two z-scores are -1.53 and 1.53
Step-by-step explanation:
To find the two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution
- Assume that z-score is between -c and c ⇒ P(-c < z < c) = the given value
- Find the value of P(z < -c or z > c) = 1 - the given value
- P(z < -c) + P(z > c) = the answer of the previous step
- 2*P(z < -c) = the answer of the previous step
- Find the value of P(z < -c)
- In the z-table having area to the left of z, look for the value closest to the value of P(z < -c) inside the table to find the closest value of z
∵ P(-c < z < c) = 87.4%
∵ 87.4% = 87.4 ÷ 100 = 0.874
∴ P(-c < z < c) = 0.874
∵ P(z > c) = 1 - 0.874 = 0.126
∴ P(z < -c) + P(z > c) = 0.126
∵ P(z > c) = P(z < -c)
∴ P(z < -c) + P(z < -c) = 0.126
∴ 2*P(z < -c) = 0.126
- Divide both sides by 2
∴ P(z < -c) = 0.063
Let us use the z-table to find the corresponding values of
z to 0.063
∵ The corresponding value of z to 0.063 = -1.53
∴ The two z-scores = -1.53 and 1.53
The attached figure for more understand
The two z-scores are -1.53 and 1.53
Learn more:
You can learn more about z-score in brainly.com/question/6270221
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