QuestionFor a Standard Normal Variable, find $P(0.58<z<1.74)$ using the provided tables.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a standard normal random variable, which means the mean ( $\mu$ ) is0 and the standard deviation ( $\sigma$ ) is1. . We are asked to find the probability that the random variable $z$ lies between0.58 and1.74.
3. We are using standard normal distribution tables to find the probabilities.

STEP 2

The probability that a standard normal random variable lies between two values is given by the cumulative distribution function (CDF) of the higher value minus the CDF of the lower value.
$(a<z<b) =(z<b) -(z<a)$

STEP 3

In this problem, we are asked to find $(0.58<z<1.74)$ . So, we need to find $(z<1.74)$ and $(z<0.58)$ using the standard normal distribution tables.

STEP 4

First, let's find $(z<1.74)$ . Look up1.74 in the standard normal distribution table. The value in the table represents the area to the left of1.74 under the standard normal curve, which is the same as $(z<1.74)$ .

STEP 5

Next, let's find $(z<0.58)$ . Look up0.58 in the standard normal distribution table. The value in the table represents the area to the left of0.58 under the standard normal curve, which is the same as $(z<0.58)$ .

STEP 6

Now, subtract $(z<0.58)$ from $(z<1.74)$ to find $(0.58<z<1.74)$ .
$(0.58<z<1.74) =(z<1.74) -(z<0.58)$

STEP 7

Plug in the values from the standard normal distribution table for $(z<1.74)$ and $(z<0.58)$ to calculate $(0.58<z<1.74)$ .
Note The actual values for $(z<1.74)$ and $(z<0.58)$ will depend on the specific standard normal distribution table used. For example, if the table gives $(z<1.74) =0.9591$ and $(z<0.58) =0.7197$ , then $(0.58<z<1.74) =0.9591 -0.7197$

STEP 8

Calculate $(0.58<z<1.74)$ .
$(0.58<z<1.74) =0.9591 -0.7197 =0.2394$ So, the probability that a standard normal random variable lies between0.58 and1.74 is approximately0.2394.

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