Use the standard normal distribution to find P(-2.25 < z < 1.25).
Use the table in the back of your book labeled something like "areas under the normal distribution." Find the above Z scores and the proportions between them and the mean. Add the two proportions.
I hope this helps. Thanks for asking.
To find the probability of a range within the standard normal distribution, we need to use a standard normal distribution table or a calculator.
Step 1: Draw the standard normal curve.
The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1.
Step 2: Identify the given range.
The given range is -2.25 < z < 1.25, where z represents the standard score or the number of standard deviations away from the mean.
Step 3: Convert the range to z-scores.
To use the standard normal distribution table, we need to convert the given values (-2.25 and 1.25) into their corresponding z-scores.
The z-score formula is: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For -2.25:
z = (-2.25 - 0) / 1
z = -2.25
For 1.25:
z = (1.25 - 0) / 1
z = 1.25
Step 4: Look up the probabilities in the standard normal distribution table.
Use the standard normal distribution table to find the probabilities corresponding to the z-scores obtained in step 3. The table provides the area under the curve to the left of the z-score.
For -2.25, we look up the probability value for -2.25 in the table. Let's assume we find the value to be 0.0122.
For 1.25, we look up the probability value for 1.25 in the table. Let's assume we find the value to be 0.8944.
Step 5: Calculate the final probability.
To find the probability of -2.25 < z < 1.25, subtract the probability of -2.25 from the probability of 1.25:
P(-2.25 < z < 1.25) = P(z < 1.25) - P(z < -2.25)
= 0.8944 - 0.0122
= 0.8822
Therefore, the probability of -2.25 < z < 1.25, using the standard normal distribution, is 0.8822.
To find the probability that a random variable from a standard normal distribution falls between two values, we need to use the standard normal distribution table or a calculator.
The given interval is -2.25 < z < 1.25.
Step 1: Find the individual probabilities for each end point of the interval.
P(z < 1.25) = 0.8944 (lookup from the standard normal distribution table)
P(z < -2.25) = 0.0122 (lookup from the standard normal distribution table)
Step 2: Calculate the probability between the two end points.
P(-2.25 < z < 1.25) = P(z < 1.25) - P(z < -2.25)
= 0.8944 - 0.0122
= 0.8822
Therefore, P(-2.25 < z < 1.25) is approximately 0.8822.