Question

Compute the probability area to the left of z=-1.25.

Answer 1

To find the probability area to the left of z=-1.25, one would look up the value in a z-table or use a calculator command such as invNorm(0.975,0,1) for Z0.025, adjusting the command accordingly. The area to the left of z=-1.25 is not provided directly here due to an apparent error in the reference material.

Step-by-step explanation:

To compute the probability area to the left of z=-1.25, we would normally use the z-table. However, the provided reference information seems to contain an error regarding the area to the left of z, which is not 0.6554 for a z-score of -1.25. Typically, you would look up the z-score of -1.25 in the z-table to find the corresponding area to the left, which represents the cumulative probability. Instead, let's use another reference provided, that is, the use of a calculator. For instance, we can use the command invNorm(0.975,0,1) on a TI-83, 83+, or 84+ calculator to find Z0.025, implying the area to the left of Z0.025 is 0.975. Here, instead, we would use invNorm(0.1056,0,1) to find the z-value when we know the left-tail area, which should be the same as locating the z-score of -1.25 in a z-table.

To determine P(x > 65), assuming this refers to a value on a standard normal distribution, we would need additional context or information about the mean and standard deviation of the distribution in question. If 65 is a value on a normal distribution with a certain mean and standard deviation, we could convert it to a z-score and then use the z-table or a calculator to find the corresponding area to the right.

Answer 2

The probability area to the left of ( z = -1.25 ) is approximately 0.1056.

Step-by-step explanation:

To compute the probability area to the left of ( z = -1.25 ), we refer to the standard normal distribution table or use a calculator. The z-score represents the number of standard deviations a data point is from the mean in a standard normal distribution. In this case, ( z = -1.25 ) means the data point is 1.25 standard deviations below the mean.

Looking up this z-score in a standard normal distribution table or using a calculator, we find the corresponding cumulative probability, which is the probability that a standard normal random variable is less than or equal to (z = -1.25 ). This value is approximately 0.1056.

In statistical terms, this probability represents the likelihood of observing a value less than or equal to ( z = -1.25 ) in a standard normal distribution. It is crucial in statistical analysis for understanding the relative position of a data point in a distribution.