Question

A variable x is normally distributed with mean 17 and standard deviation 7.Round your answers to the nearest hundredth as needed.a) Determine the z-score for x = 20.2b) Determine the z-score for x = 15.zc) What value of has a z-score of 1?d) What value of x has a z-score of -0.1?e) What value of x has a z-score of 0?=

Answer 1

a) The z-score for x = 20.2 is 0.486. b) The z-score for x = 15 is -0.286. c) The value of x that has a z-score of 1 is 24. d) The value of x that has a z-score of -0.1 is 16.3. e) The value of x that has a z-score of 0 is 17.

Step-by-step explanation:

a) To determine the z-score for x = 20.2, we use the formula z = (x - mean) / standard deviation. Plugging in the values, we get z = (20.2 - 17) / 7 = 0.486.

b) To determine the z-score for x = 15, we use the same formula. Plugging in the values, we get z = (15 - 17) / 7 = -0.286.

c) To find the value of x that has a z-score of 1, we rearrange the formula and solve for x. Plugging in the values, we have 1 = (x - 17) / 7. Solving for x, we get x = 24.

d) To find the value of x that has a z-score of -0.1, we use the formula z = (x - 17) / 7 and plug in the z-score value. Rearranging the formula and solving for x, we get x = 16.3.

e) To find the value of x that has a z-score of 0, we use the formula z = (x - 17) / 7. Plugging in the z-score value of 0 and solving for x, we get x = 17.

Answer 2

Given

`\begin{gathered} \text{ mean }\mu=17 \\ \\ \text{ standard deviation }\sigma=7 \end{gathered}`

The Z score is given by the formula;

`Z=(X-\mu)/(\sigma)`

(a)

`Z=(20-17)/(7)\approx0.43\text{ \lparen nearest hundredth\rparen}`

(b)

`Z=(15-17)/(7)\approx-0.29\text{ \lparen nearest hundredth\rparen}`

(c)

when Z = 1

`\begin{gathered} \Rightarrow1=(X-17)/(7) \\ \\ \Rightarrow7=X-17 \\ \\ \Rightarrow X=7+17 \\ \\ \Rightarrow X=24 \end{gathered}`

when Z = -0.1

`\begin{gathered} \Rightarrow-0.1=(X-17)/(7) \\ \\ \Rightarrow-(7)/(10)=X-17 \\ \\ \Rightarrow X=17-(7)/(10) \\ \\ \Rightarrow X=16.3 \end{gathered}`

When Z = 0

`\begin{gathered} \Rightarrow0=(X-17)/(7) \\ \\ \Rightarrow0=X-17 \\ \\ \Rightarrow X=17 \end{gathered}`