# Understanding Probability in Standard Normal DistributionThe standard normal distribution is a crucial concept in statistics, often used to represent real-valued random variables in standard form. In this lesson, we'll assess the probability that a random variable with a standard normal distribution takes on a specified value range. Let's explore the following scenarios:### a) Probability Between 0.87 and 1.28To find this probability, locate the z-scores 0.87 and 1.28 on the standard normal distribution table. Subtract the cumulative probability of 0.87 from that of 1.28 to determine the probability within this range.### b) Probability Between -0.34 and 0.62Similarly, find the cumulative probabilities for z-scores -0.34 and 0.62. The probability between these values is the difference between their cumulative probabilities.### c) Probability Greater than 0.85To calculate the probability of obtaining a value greater than 0.85, find the cumulative probability for 0.85 and subtract it from 1.### d) Probability Greater than -0.65For this probability, use the cumulative distribution function to find the cumulative probability for -0.65 and again subtract it from 1 to determine the probability of getting values greater than -0.65.These calculations are foundational for anyone studying statistics and help illustrate how data is distributed under the normal curve. With these insights, you can interpret probability and data behavior within specified ranges effectively.

The z score follows standard normal distribution with mean 0 and standard deviation 1.

Answered: Find the probability that a random…

Find the probability that a random variable having the standard normal distribution will take on a value: a) Between 0.87 and 1.28 b) Between -0.34 and 0.62 c) Greater than 0.85 d) Greater than -0.65

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Estimation

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# Understanding Probability in Standard Normal Distribution

The standard normal distribution is a crucial concept in statistics, often used to represent real-valued random variables in standard form. In this lesson, we'll assess the probability that a random variable with a standard normal distribution takes on a specified value range. Let's explore the following scenarios:

### a) Probability Between 0.87 and 1.28

To find this probability, locate the z-scores 0.87 and 1.28 on the standard normal distribution table. Subtract the cumulative probability of 0.87 from that of 1.28 to determine the probability within this range.

### b) Probability Between -0.34 and 0.62

Similarly, find the cumulative probabilities for z-scores -0.34 and 0.62. The probability between these values is the difference between their cumulative probabilities.

### c) Probability Greater than 0.85

To calculate the probability of obtaining a value greater than 0.85, find the cumulative probability for 0.85 and subtract it from 1.

### d) Probability Greater than -0.65

For this probability, use the cumulative distribution function to find the cumulative probability for -0.65 and again subtract it from 1 to determine the probability of getting values greater than -0.65.

These calculations are foundational for anyone studying statistics and help illustrate how data is distributed under the normal curve. With these insights, you can interpret probability and data behavior within specified ranges effectively.

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