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
frozen [14]
2 years ago
13

Data are drawn from a bell-shaped distribution with a mean of 25 and a standard deviation of 4. There are 1,000 observations in

the data set.
a. Approximately what percentage of the observations are less than 33?
b. Approximately how many observations are less than 33?
Mathematics
1 answer:
Delicious77 [7]2 years ago
6 0

Answer:

a. 97.72% of the observations are less than 33

b. Approximately 977 observations are less than 33.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 25 and a standard deviation of 4.

This means that \mu = 25, \sigma = 4

a. Approximately what percentage of the observations are less than 33?

The proportion is the p-value of Z when X = 33. So

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

Z = \frac{33 - 25}{4}

Z = 2

Z = 2 has a p-value of 0.9772

0.9772*100% = 97.72%

97.72% of the observations are less than 33.

b. Approximately how many observations are less than 33?

Out of 1000:

0.9772*1000 = 977.2

Approximately 977 observations are less than 33.

You might be interested in
1. What is the probability of getting a number greater than 2 on two rolls of a six-sided die both times?
prisoha [69]

Answer:

For this question, the options are written the wrong way. In each of the answers below, the correct form of the question will be added.  

The answers are:

1. e) 4/9

2. a) 1/16

3. 980 girls

4. c) 2/3

5. d) 1/13

6. a) 42 boys

7. d) 1/21

8. b) 1/6

Step-by-step explanation:

1. What is the probability of getting a number greater than 2 on two rolls of a six-sided die both times?

a) 4/3

b) 2/6

c) 4/6

d) 3/6

e) 4/9

The correct answer is e) 4/9 because the probability of getting a number greater than 2 in two rolls is 4/6 * 4/6 =16/36 = 4/9

2. A fair coin is tossed four times. What is the probability that it will be heads every time?

a) 1/16

b) 4/2

c) 2

d) 4/16

e) 1

The correct answer is a) 1/16 because the probability of each time that the coin is tossed is 1/2, and for 4 tosses is 1/2*1/2*1/2*1/2 = 1/16

3. The ratio of the number of girls to the number of boys was 2 to 5. If 2,450 students were present, how many were girls and how many were boys?

The correct answer is 980 girls, because 2450*2/5 = 980

4. A die is rolled twice. What is the probability of rolling a 5 or getting an even number?

a) 3/1

b) 1/12

c) 2/3

d) 1/3

If the die is rolled twice there are 12 possible outcomes and 8 of those outcomes can be 5 or an even number. The probability is 8/12 = 2/3

5. If one card is drawn from a standard deck, what is the probability of getting a jack?

a) 4/13

b) 1/52

c) 52

d) 1/13

e) 4

In a standard deck, there are 13 jack cards, the probability of getting a jack the first time is 1/13

6. There are 210 boys trying out for football. If 20% made the team, how many were chosen?

a) 42

b) 10

c) 4200

d) 105

e) 20

The number of boys that will be picked for the team is 210*20% = 42

7. From 42 boys who made the team, one will be chosen as kicker and one will be chosen as quarterback. What is the probability of being chosen as the kicker or the quarterback?

a) 2/21

b) 1/42

c) 2

d) 1/21

e) 42

The probability of getting picked for one of the 2 positions is 2/42 = 1/21

8. Two dice are rolled. There are 36 possible outcomes of rolling two dice. What is the probability of getting a total of seven on one roll?

a) 7

b) 1/6

c) 0

d) 7/36

e) 1/36

There are 6 ways of getting a sum of 7 tossing 2 dice, 1+6, 6+1, 2+5, 5+2, 3+4, 4+3. The probability is 6/36 = 1/6

3 0
3 years ago
The vertices of a swimming pool are E(5, 5), F(5, 20), G(35, 20), and H(35, 5). The endpoints of a line that divides the pool in
sleet_krkn [62]

Answer:

Step-by-step explanation:

Download pdf
3 0
3 years ago
NEED HELP!! NO Absurd answers!
Orlov [11]

Answer:

Approximately 94% of theaters charge more than $10 to see the movie.

Step-by-step explanation:

Use a calculator with distribution functions such as normalcdf(

Here we have normalcdf(10,1000,11.80, 1.15) = 0.941

Approximately 94% of theaters charge more than $10 to see the movie.  This agrees with the last answer choice.

8 0
3 years ago
ASAP<br> -will mark brianist
Amiraneli [1.4K]

Answer:

20-12

35-21

40-24

Step-by-step explanation:

You times both numbers by the same value

5 0
3 years ago
Read 2 more answers
HELP ME PLS?? <br> 2 divided by 1/2= ??
Gennadij [26K]
The answer is 4
Because 0.5 times 4 is 2
5 0
3 years ago
Read 2 more answers
Other questions:
  • X-10%=y<br> y-30%=z<br> z-p=42<br> x=?
    13·1 answer
  • It says in abc, What is m
    8·1 answer
  • Find the quotient of 575 and 14 using partial quotients
    5·1 answer
  • Please answer this questions ​
    15·1 answer
  • Choose the inequality that represents the following graph.
    6·2 answers
  • Help me plsss it’s due in five minuted
    13·1 answer
  • Part C
    10·2 answers
  • In an experiment, the temperature of a sample is measured as 16 degrees Celsius. If the percent error is 0.75%, how can you repo
    10·1 answer
  • If <img src="https://tex.z-dn.net/?f=f%28x%29%3D%5B%5Bx%2B2%5D%5D" id="TexFormula1" title="f(x)=[[x+2]]" alt="f(x)=[[x+2]]" alig
    11·2 answers
  • let P = (x,y) and Q = (1, 5). suing formula that you know for slope write an eqation in these terms of coordinates that says tha
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!