1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natka813 [3]
2 years ago
6

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Ro

und your answers to four decimal places.) (a) P(0 ≤ Z ≤ 2.87) .9979 Incorrect: Your answer is incorrect. (b) P(0 ≤ Z ≤ 2) .9772 Incorrect: Your answer is incorrect. (c) P(−2.20 ≤ Z ≤ 0) .0139 Incorrect: Your answer is incorrect. (d) P(−2.20 ≤ Z ≤ 2.20) .9633 Incorrect: Your answer is incorrect. (e) P(Z ≤ 1.01) .8438 Correct: Your answer is correct. (f) P(−1.95 ≤ Z) .0256 Incorrect: Your answer is incorrect. (g) P(−1.20 ≤ Z ≤ 2.00) .8621 Correct: Your answer is correct. (h) P(1.01 ≤ Z ≤ 2.50) 0.15 Correct: Your answer is correct. (i) P(1.20 ≤ Z) .8849 Incorrect: Your answer is incorrect. (j) P(|Z| ≤ 2.50) .9938 Incorrect: Your answer is incorrect.

Mathematics
2 answers:
Tamiku [17]2 years ago
8 0

Answer:

a) 0.49795

b) 0.47725

c) 0.4861

d) 0.9722

e) 0.84375

f) 0.02559

g) 0.86218

h) 0.15004

i) 0.11507

j) 0.9876

Step-by-step explanation:

attached is the statistical table for your reference.

(a) P(0 ≤ Z ≤ 2.87)

    P( Z ≤ 2.87) - P(Z ≤ 0)       ⇒From statistical table of positive z values

    = 0.99795 - 0.5 = 0.49795

(b) P(0 ≤ Z ≤ 2)

    P( Z ≤ 2) - P(Z ≤ 0)       ⇒From statistical table of positive z values

    = 0.97725 - 0.5 = 0.47725

(c) P(−2.20 ≤ Z ≤ 0)

    P( Z ≤ 0) - P(Z ≤ -2.20)       ⇒From statistical table of positive&negative z values

    = 0.5 - 0.01390 = 0.4861

(d) P(−2.20 ≤ Z ≤ 2.20)

    P( Z ≤ 2.20) - P(Z ≤ -2.20)       ⇒From statistical table of positive&negative z values

    = 0.98610 - 0.01390 = 0.9722

(e) P(Z ≤ 1.01)       ⇒From statistical table of positive z values

    0.84375

(f) P(−1.95 ≤ Z)

   P(Z ≥ −1.95)

   = 1 - P(Z < 1.95)       ⇒From statistical table of positive z values

   = 1 - 0.97441 = 0.02559

(g) P(−1.20 ≤ Z ≤ 2.00)

    P( Z ≤ 2.00) - P(Z ≤ -1.20)       ⇒From statistical table of positive&negative z values

    = 0.97725 - 0.11507 = 0.86218

(h) P(1.01 ≤ Z ≤ 2.50)

    P( Z ≤ 2.50) - P(Z ≤ 1.01)       ⇒From statistical table of positive z values

    = 0.99379 - 0.84375 = 0.15004

(i) P(1.20 ≤ Z)

   P(Z ≥ 1.20)

   = 1 - P(Z < 1.20)       ⇒From statistical table of positive z values

   = 1 - 0.88493 = 0.11507

(j) P(|Z| ≤ 2.50)

   P(-2.50 ≤ Z ≤ 2.50)

   P(Z ≤ 2.50) - P(Z ≤ -2.50)      ⇒From statistical table of positive&negative z values

   = 0.9938 - 0.0062

   = 0.9876

Download pdf
puteri [66]2 years ago
7 0

Answer:

(a) P(0 ≤ Z ≤ 2.87)=0.498

(b) P(0 ≤ Z ≤ 2)=0.477

(c) P(−2.20 ≤ Z ≤ 0)=0.486

(d) P(−2.20 ≤ Z ≤ 2.20)=0.972

(e) P(Z ≤ 1.01)=0.844

(f) P(−1.95 ≤ Z)=0.974

(g) P(−1.20 ≤ Z ≤ 2.00)=0.862

(h) P(1.01 ≤ Z ≤ 2.50)=0.150

(i) P(1.20 ≤ Z)=0.115

(j) P(|Z| ≤ 2.50)=0.988

Step-by-step explanation:

(a) P(0 ≤ Z ≤ 2.87)

In this case, this is equal to the difference between P(z<2.87) and P(z<0). The last term is substracting because is the area under the curve that is included in P(z<2.87) but does not correspond because the other condition is that z>0.

P(0 \leq z \leq 2.87)= P(z

(b) P(0 ≤ Z ≤ 2)

This is the same case as point a.

P(0 \leq z \leq 2)= P(z

(c) P(−2.20 ≤ Z ≤ 0)

This is the same case as point a.

P(-2.2 \leq z \leq 0)= P(z

(d) P(−2.20 ≤ Z ≤ 2.20)

This is the same case as point a.

P(-2.2 \leq z \leq 2.2)= P(z

(e) P(Z ≤ 1.01)

This can be calculated simply as the area under the curve for z from -infinity to z=1.01.

P(z\leq1.01)=0.844

(f) P(−1.95 ≤ Z)

This is best expressed as P(z≥-1.95), and is calculated as the area under the curve that goes from z=-1.95 to infininity.

It also can be calculated, thanks to the symmetry in z=0 of the standard normal distribution, as P(z≥-1.95)=P(z≤1.95).

P(z\geq -1.95)=0.974

(g) P(−1.20 ≤ Z ≤ 2.00)

This is the same case as point a.

P(-1.20 \leq z \leq 2.00)= P(z

(h) P(1.01 ≤ Z ≤ 2.50)

This is the same case as point a.

P(1.01 \leq z \leq 2.50)= P(z

(i) P(1.20 ≤ Z)

This is the same case as point f.

P(z\geq 1.20)=0.115

(j) P(|Z| ≤ 2.50)

In this case, the z is expressed in absolute value. If z is positive, it has to be under 2.5. If z is negative, it means it has to be over -2.5. So this probability is translated to P|Z| < 2.50)=P(-2.5<z<2.5) and then solved from there like in point a.

P(|z|

You might be interested in
IN<br> 4. Solve: 9p² -3 = 7
Vlad1618 [11]
Square root of 10 over 3

8 0
3 years ago
If the simple interest on ​$7000 for 3 years is ​$1890​, then what is the interest​ rate?
hoa [83]

Answer:

0.09 or 9%

Step-by-step explanation:

I = Prt

Given:

I = 1890

P = 7000

t = 3

Work:

I = Prt

r = I/(Pt)

r = 1890/(7000 x 3)

r = 1890/21000

r = 0.09

4 0
2 years ago
Please answer correctly i need help with these.
vladimir1956 [14]
H = positive (14) because -98 / -7 is 14
U = is (-144) because it has u multiply 6 instead of dividing to remove it. If you do it ot one side you must do it to all other sides.
Q = 18 * 5 is (90)
3 0
2 years ago
Read 2 more answers
Can u pls help I need a good grade
almond37 [142]

Answer:

15?

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Hello! Any help is appreciated (:
lara [203]

Answer:

yes

Step-by-step explanation:

This relation is a function

Each input value goes to only one output value so the relation is a function

6 0
3 years ago
Read 2 more answers
Other questions:
  • How do u divide 144 and 4.5
    12·1 answer
  • jordan is mailing a package at the post office .The box measures 8 3/4 inches long ,2 6/7 inches wide and 5 inches high.What is
    11·2 answers
  • 2. The area of the rectangle is 224 square inches. The length of the rectangle is 14
    14·1 answer
  • Please, I just don't now waaaaa
    15·1 answer
  • Select the correct answer
    8·1 answer
  • The mean housing price for an area is $135,000 with a standard of $45,000 but is not normally distributed. According to the Cent
    6·1 answer
  • Translate the following written expression into a mathematical expression. Then, find the expression's value when w = 6 and x =
    6·1 answer
  • Is the mistake one two three or is their no mistake
    6·1 answer
  • 35°<br> X=<br> solve for the missing angles
    14·1 answer
  • What are the dimensions of the rectangle shown on the coordinate plane?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!