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stealth61 [152]
4 years ago
9

Which of the following situations results in a sum of 1 1/2 ? Select all that apply

Mathematics
1 answer:
NemiM [27]4 years ago
5 0

Answer:

The answer is: B, C, and F.

Step-by-step explanation:

A. No.

3 1/3 - 1 5/6 =

10/3 - 11/6 =

20/6 - 11/6 =

9/6 = 2/3

B. Yes.

1 1/4 + 1/4 = 1 1/2

C. Yes.

6 1/2 - 8 = 1 1/2

D. No.

4 1/4 - 1 3/4 =

17/4 - 7/4 =

10/4 =

5/2 =

2 1/2

E. No

5/8 + 7/8 =

13/8 =

1 5/8

F. Yes.

2 1/4 - 3/4 =

9/4 - 3/4 =

6/4 =

3/2 =

1 1/2

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Y is a random variable that is distributed N(-16, 1.21). Find k such that Prob(-15.043 &lt; Y ≤ k) = 0.1546. (Round your answer
IgorLugansk [536]

Transform <em>Y</em> to <em>Z</em>, which is distributed N(0, 1), using the formula

<em>Y</em> = <em>µ</em> + <em>σZ</em>

where <em>µ</em> = -16 and <em>σ</em> = 1.21.

Pr[-15.043 < <em>Y</em> ≤ <em>k</em>] = 0.1546

Pr[(-15.043 + 16)/1.21 < (<em>Y</em> + 16)/1.21 ≤ (<em>k</em> + 16)/1.21] = 0.1546

Pr[0.791 < <em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.1546

Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] - Pr[<em>Z</em> < 0.791] = 0.1546

Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] = 0.1546 + Pr[<em>Z</em> < 0.791]

Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.1546 + 0.786

Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.940

Take the inverse CDF of both sides (<em>Φ(x)</em> denotes the CDF itself):

(<em>k</em> + 16)/1.21 ≈ <em>Φ⁻¹</em> (0.940) ≈ 1.556

Solve for <em>k</em> :

<em>k</em> + 16 = 1.21 • 1.556

<em>k</em> ≈ -14.118

8 0
3 years ago
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