In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z = -1.95

검증된 단계별 안내

Step 1: Understand the problem. You are tasked with finding the area under the standard normal curve to the left of z = -1.95. This represents the cumulative probability for a z-score of -1.95 in a standard normal distribution.

Step 2: Recall that the standard normal distribution is symmetric about the mean (z = 0), and the total area under the curve is 1. The area to the left of a given z-score represents the cumulative probability up to that z-score.

Step 3: Use the z-score table (also called the standard normal table) or technology (such as a graphing calculator or statistical software) to find the cumulative probability corresponding to z = -1.95. The table or software will provide the area to the left of this z-score.

Step 4: If using a z-score table, locate the row corresponding to -1.9 and the column corresponding to 0.05 (since -1.95 = -1.9 + 0.05). The intersection of this row and column gives the cumulative probability.

Step 5: If using technology, input the z-score of -1.95 into the appropriate function (e.g., 'normalcdf' on a calculator or a similar function in statistical software) to directly obtain the cumulative probability. This value represents the area under the curve to the left of z = -1.95.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Standard Normal Distribution

The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1. It is used to describe how data points are distributed in a standardized way, allowing for comparison across different datasets. The area under the curve represents probabilities, with the total area equaling 1.

Z-scores

A Z-score indicates how many standard deviations a data point is from the mean of a distribution. It is calculated by subtracting the mean from the data point and dividing by the standard deviation. In the context of the standard normal distribution, a Z-score of -1.95 means the value is 1.95 standard deviations below the mean.

Area Under the Curve

The area under the curve of a probability distribution represents the likelihood of a random variable falling within a particular range. For the standard normal distribution, this area can be found using Z-tables or technology, such as statistical software, to determine probabilities associated with specific Z-scores.

In Exercises 7–18, find the indicated area under the standard normal curve. If convenient, use technology to find the area.To the left of z = -1.95