Find the number z such that the proportion of observations that are less than z in a standard normal distribution is 0.5414. (b) find the number z such that 65.91% of all observations from a standard normal distribution are greater than z. (a)

Part (a) The value of Z is 0.10396. Part (b) The value of Z is 0.410008.

Step-by-step explanation:

Consider the provided information.

Part (a)

In order to find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.5414, simply find 0.5414 in the table and search for the appropriate Z-value.

Now, observing the table it can be concluded that the value of Z is 0.10396.

Part (b)

Consider the number 65.91%

The above number can be written as 0.6591.

Now, find 0.6591 in the table and search for the appropriate Z-value.

By, observing the table it can be concluded that the value of Z is 0.410008.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).