Final answer:
To find the value of z such that the area to the right of z is 0.1335, we can use the z-table. The z-score that corresponds to the area of 0.8665 is approximately 1.10.
Explanation:
The standard normal curve, also known as the Z-distribution or Z-curve, is a special case of the normal distribution with a mean (μ) of 0 and a standard deviation (σ) of 1. The equation for the probability density function (PDF) of the standard normal distribution is given by:
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(
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=
1
2
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−
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2
2
,
f(z)=
2π
1
e
−
2
z
2
,
where:
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z is a standard score or Z-score (measuring how many standard deviations an individual data point is from the mean),
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π is the mathematical constant pi (approximately 3.14159),
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e is the mathematical constant approximately equal to 2.71828.
The standard normal curve is symmetric about the mean (0) and follows a bell-shaped curve. It is widely used in statistics and probability theory for various applications, including hypothesis testing and confidence intervals.
When working with the standard normal distribution, statisticians often use Z-scores to standardize values from a normal distribution with any mean and standard deviation to the standard normal curve
To find the value of z such that the area to the right of z is 0.1335 in a standard normal curve, we can use the z-table. The z-table shows that the area to the left of z is 1 - 0.1335 = 0.8665. From the z-table, we can find the z-score that corresponds to the area of 0.8665, which is approximately 1.10.