Question

(i) The mean of a normal probablity distribution is 60 and the standard deviation is 5. 95. 44 percent of observations lie between 50 and 75. (ii) A z-value of −2. 00 indicates that corresponding X value lies to the left of the mean. (iii) One of the properties of the normal curve is that it gets cioser to the horizontal axis, but never touches it This property of the normal curve is called asymptotic. Muttiple Choice (i) is a conect statement but not (9) or fili. (7) and (in) ate cocrect statements but not (i) 0. (in). And (iil) are all correct statements. (1) and (ii) are correct tratements but not iini (ii) and (i) are correct siatements but not (i) The amount spent per month by employees for parking at a municipal lot is normally distributed with a mean of $220 and a standard deviation of $15. (Round the final answers to 2 decimal places. ) a. About what percentage of the observations lle between $205 and $235 ? Percentage of observations b. About what percentage of the observations lie between $190 and $250 ? Percentage of observations c. About what percentage of the observations lle between $175 and $265 ? Percentage of observations

Answer 1

Explanation:

a) To find the percentage of observations that lie between $205 and $235, we need to calculate the area under the normal distribution curve between these two values.

First, we need to convert the dollar values to z-scores using the formula:

z = (x - mean) / standard deviation

For $205:

z1 = ($205 - $220) / $15 = -1

For $235:

z2 = ($235 - $220) / $15 = 1

Next, we look up the corresponding areas under the standard normal distribution curve for z1 = -1 and z2 = 1. This can be done using a z-table or a statistical software.

The percentage of observations between $205 and $235 is the difference between these two areas.

b) Similarly, to find the percentage of observations that lie between $190 and $250, we need to convert these values to z-scores and calculate the corresponding areas under the normal distribution curve.

For $190:

z1 = ($190 - $220) / $15 = -2

For $250:

z2 = ($250 - $220) / $15 = 2

We can then find the difference between the areas under the curve for z1 = -2 and z2 = 2.

c) To find the percentage of observations that lie between $175 and $265, we follow the same steps as above, converting the values to z-scores and calculating the corresponding areas under the normal distribution curve.

For $175:

z1 = ($175 - $220) / $15 = -3

For $265:

z2 = ($265 - $220) / $15 = 3

We can then find the difference between the areas under the curve for z1 = -3 and z2 = 3.

Please note that the exact values for the percentages will depend on the specific calculations using the z-table or statistical software.