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
Anon25 [30]
2 years ago
9

Find the following probabilities for the standard normal random variable z: a. P(−1.36 ≤ z ≤ 1.38)= ________ b. P(−2.27 ≤ z ≤ 1.

64)= ________ c. P(z ≤ 1.33)=________ d. P(z > −0.68)=_____
Mathematics
2 answers:
Nesterboy [21]2 years ago
6 0

Answer:

a) 0.8293

b) 0.9379

c) 0.9082

d) 0.7517

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

a. P(−1.36 ≤ z ≤ 1.38)=

This is the pvalue of Z = 1.38 subtracted by the pvalue of Z = -1.36

Z = 1.38 has a pvalue of 0.9162

Z = -1.36 has a pvalue of 0.0869

0.9162 - 0.0869 = 0.8293

b. P(−2.27 ≤ z ≤ 1.64)

Same logic as a.

Z = 1.64 has a pvalue of 0.9495

Z = -2.27 has a pvalue of 0.0116

0.9495 - 0.0116 = 0.9379

c. P(z ≤ 1.33)=

This is the pvalue of Z = 1.33.

Z = 1.33 has a pvalue of 0.9082

d. P(z > −0.68)=

This is 1 subtracted by the pvalue of Z = -0.68. So

Z = -0.68 has a pvalue of 0.2483

1 - 0.2483 = 0.7517

Llana [10]2 years ago
3 0

Answer:

Step-by-step explanation:

a) P(−1.36 ≤ z ≤ 1.38)

For z = - 1.36,

The corresponding probability from the normal distribution table is 0.08691

For z = 1.38

The corresponding probability from the normal distribution table is 0.9162

Therefore,

P(−1.36 ≤ z ≤ 1.38)

= 0.9162 - 0.08691 = 0.82929

b) P(−2.27 ≤ z ≤ 1.64)

For z = - 2.27

The corresponding probability from the normal distribution table is

0.0116

For z = 1.64,

The corresponding probability from the normal distribution table is

0.9495

Therefore,

P(−2.27 ≤ z ≤ 1.64)

= 0.9495 - 0.0116 = 0.9379

c) P(z ≤ 1.33)

For z = 1.33

The corresponding probability from the normal distribution is 0.9082

Therefore,

P(z ≤ 1.33) = 0.9082

d) P(z > −0.68) = 1 - P(z ≤ −0.68)

For z = - 0.68

The corresponding probability from the normal distribution is 0.2482

Therefore,

P(z > −0.68) = 1 - 0.2482 = 0.7518

You might be interested in
To make lemonade, you used one quart of water, one pint of lemon juice, and 9 ounces of your secret ingredient: honey. How much
WITCHER [35]
To solve this problem you must follow the proccedure shown below:

 1. Amount of lemonade in pints:

 1 <span>quart of water=2 pints
 1 pint of lemon
 (9  ounces of honey)(0.0625 pints/1 ounce)=0.56 pints

 Total in pints=2 pints+1 pint+0.56 pints
 Total in pints=3.56 pints

 2. </span>Amount of lemonade in<span> cups:

 Total in cups=(3.56 pints)(2 cups/1 pint)
 Total in cups=7.12 cups

 
3. </span>Amount of lemonade in<span> ounces:

 Total in ounces=(7.12  cups)(8 ounces/1 cup)
 Total in ounces=56.96 ounces</span>
4 0
3 years ago
Please help math thank you
Alina [70]

a: 30

b:40

c:78

d:36

e:20

f:96

5 0
3 years ago
Read 2 more answers
Select the correct<br> function<br> that represents<br> this data.
lidiya [134]

Answer:

f(x) = -5x - 2

Step-by-step explanation:

Plug in the first set of values into each possible equation. Whichever equation yields the correct ouputs (y-values) for ALL input (x-values) is the correct answer. For the function f(x) = -5x - 2,  f(-2) = 8, f(-1) = 3 and so on... So f(x) = -5x - 2 is the correct answer!

Hope this helps!

5 0
2 years ago
If 2x+y=8 and x-1=y then what is y? Please be detailed I want to know more then just the answer but how to solve
IgorLugansk [536]
This is Bridge Algebra 2 stuff. Well you see that 2x+y=8 and x-1=y. To slove for y you have to slove for x first to find y. So 2x+x-1=8 ( the reason I did that is because there is a y in that equation and I placed it on that equation) now lets slove this equation for x. So 3x-1=8( I add 2x with x) 3x=9 ( I made -1 a positive one and add it to 8) x=3 ( I divided 9/3 to get 3). Now that you have slove x we will use x to slove for y. So 3-1=y, 2=y. Your answer is y=2.
4 0
3 years ago
What is the surface area of this design?
vichka [17]

Answer:

280in

Step-by-step explanation:

10×6=60

60×2=<u>120</u>

6×10=<u>60</u>

4×4=16

16×2=<u>32</u>

4×6=<u>24</u>

4×4=<u>16</u>

6×6=<u>36</u>

<u>120+60+32+24+16+36=280</u>

<u />

4 0
3 years ago
Other questions:
  • What is 5 17/20 as a decimals
    11·2 answers
  • If the clock was divided into equal fractional parts every five minutes what fraction is 5 mins= hour
    13·1 answer
  • Can someone please help with numbers 14 and 15 please !!! Thank you
    5·1 answer
  • PLEASE HELP ME!!! Thank you SO MUCH! Explain your answer
    5·1 answer
  • If anyone needs tutoring or help on any homework from any subject up to 8th or 9th grade, you can join my rem__ind and I will tr
    11·1 answer
  • 1. two lines meet at a point. set up and solve an equation to find the value of x
    15·1 answer
  • Please help me on this math problem
    9·1 answer
  • Three is subtracted from a number, and then the difference is divided by eleven. The result is twelve. What is the
    15·1 answer
  • A clownfish is 2 meters below the surface of the ocean. How does its distance from the surface compare to the vertical distance
    13·1 answer
  • A translation does not maintain congruency.<br> A. True<br> B. False
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!