What is the z-score with a confidence level of 95% when finding the margin of error for the mean of a normally distributed population from a sample? 0.99 1.65 1.96 2.58

For a confidence interval of 95%, z is 1.96

Step-by-step explanation:

A z-score, also called as standard score, indicates how many standard deviations away an element is from the mean. z-score can be calculated from the following formula,

where,

X = Raw score,

μ = mean,

σ = standard deviation.

For a confidence interval of 95%, we take z as 1.96

1.96

We will answer what is the value of the Z-score with a confidence level of 95% when finding the margin of error for the mean of a normally distributed population from a sample.

Z represents the value from the standard normal distribution for the selected confidence level.

See below, Z-scores for commonly used confidence intervals.

Thus, the Z-score with a confidence level of 95% is

Notes:

A confidence level of 95% (or confidence intervals) mean that if we take 100 different samples and calculate 95% confidence intervals for each sample, then about 95 out of 100 confidence intervals (CI) will contain the true mean value (μ).  

In practice, we choose a random sample and produce a confidence interval, which may or may not contain the true mean. The observed interval may be more or less than μ. As a result, 95% CI represents the range of possible precise and unknown parameters.

The formulas for confidence levels for the population mean depend on the sample size and are given below.

Confidence Intervals for μ

With,

In general, the relationship between the margin of error and the sample size is as follows:

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step-by-step explanation:

if it is $10, then the price is 14.

take 40% of the cost, and then add the cost.

40% of 10 = 4

4+10 = 14.

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step-by-step explanation: