Multi-Step Two friends compare the amount of change they

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 17. Use the empirical rule

Citrus2011 [14]

Answer:

(a) 95% of people has an IQ score between 66 and 134.

(b) 5% of people has an IQ score less than 66 or greater than 134.

(c) 2.5% of people has an IQ score greater than 134.

Step-by-step explanation:

We are given that Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 17.

Let X = Scores of an IQ test

So, X ~ Normal( $\mu=100, \sigma^{2} = 17^{2}$ )

Now, the Empirical rule states that;

68% of the data values lies within one standard deviation of the means.
95% of the data values lies within two standard deviation of the means.
99.7% of the data values lies within three standard deviation of the means.

That is; [ $\mu-\sigma,\mu+\sigma$ ] = [ $100-17,100+17$ ]

= $[83,117]$

[ $\mu-2\sigma,\mu+2\sigma$ ] = [ $100-34,100+34$ ]

= $[66,134]$

[ $\mu-3\sigma,\mu+3\sigma$ ] = [ $100-51,100+51$ ]

= $[49,151]$

(a) Percentage of people that has an IQ score between 66 and 134 is given by = P(66 < X < 134)

As seen above this value lies in the second category which means that 95% of people that has an IQ score between 66 and 134.

(b) Percentage of people that has an IQ score less than 66 or greater than 134 is given by;

As we know that 95% of the data values lies within 66 and 134, so the percentage of people that has an IQ score less than 66 or greater than 134 is = 100% - 95% = 5%.

(c) Since it has been calculated above that 5% of people has an IQ score less than 66 or greater than 134 which means half of these people will lie below score of 66 and half of these will lie above score of 134.

SO, percentage of people that has an IQ score greater than 134 = $\frac{5\%}{2}$ = 2.5%

Hence, 2.5% of people has an IQ score greater than 134.

3 0

3 years ago

Find the percent of each number 30% of 80

Wewaii [24]

30% of 80
30% = 0.3
0.3 • 80 is the same as 30% of 80.
0.3 • 80 = 24

30% of 80 is 24.

Hope this helps!

3 0

3 years ago

Five times the difference of a number and two is seven more than that number

prisoha [69]

Answer: The number is: 4 ¼ ; or, write as 4.25 .
_____________________________________________
Explanation:
_______________
We set up the problem as:
_____________________________

5(x − 2) = 7+ x ; Solve for "x" (our "unknown number"; which is the answer).
____________________________________________________
Using the "distributive property of multiplication" :
____________________________________________________
a*(b + c) = ab + ac ; AND:

a* (b − c) = ab − ac ;
_____________________________________________________
Let us take the "left-hand side" of our equation and expand it:
_______________________________________
5(x − 2) = (5*x) − (5*2) = 5x − 10 ;
_________________________________________
and rewrite the equation; substitute our "expanded value" for the "left-hand side";
________________________________
→ 5(x − 2) = 7+ x ; ↔ 5x − 10 = 7+ x ;
____________________________________
Now, subtract "x" from EACH SIDE of the equation; & add "10" to EACH SIDE of the equation;
________________________________________________
→ 5x − 10 − x + 10 = 7+ x − x + 10 ;
_______________________________________________
→ to get: 4x = 17 ;
________________________________________________
→ Now, divide EACH side of the equation by "4"; to isolate "x" on one side of the equation; and to solve for "x" (our answer);
________________________________________
→ 4x / 4 = 17 / 4;
__________________________
→ x = 17/4 = 17 ÷ 4 = 4 ¼ ; or, write as 4.25 .
_________________________________________
→ Answer: The number is: 4 ¼ ; or, write as 4.25 .
_____________________________________________
→Let us check our answer:
_____________________________________________
"Five times the difference of a number and 2" ;
_____________________________________________
→ 5* (x − 2) = 5 * (4.25 − 2) = 5 * (2.25) = 11.25 ;

→ Is "11.25" , SEVEN MORE THAN 4.25??
_________________________________________
→ 11.25 − 4.25 =?? 7 ??? Yes!
__________________________________________

3 0

3 years ago

PLS HELP MEEEEEEEE PLS I NEED THIS ASAP

ki77a [65]

Answer:the first one is 16 and the second one I don’t know and it’s kinda hard to see

5 0

3 years ago

Read 2 more answers

Jenette rides her bike to the bus station where she barely makes it in time to catch the bus to work. She spends half an hour on

aleksklad [387]

Answer:

The rate of the bike is approximately 23.14 mph

The rate of the bus is approximately 62.14 mph

Step-by-step explanation:

The given parameters are;

The time Janette spends on her bike to get to bus station = Half an hour = 0.5 hours = 30 minutes

The time Janette spends on the bus on her way to work = Two-thirds of an hour = 2/3 hours

The speed of the bus = 39 mph + The speed with which Janet travels on her bike

The total distance from her home to her work = 40 miles

To answer the question, let the speed with which Janet travels on her bike in miles per hour = x = the rate of the bike

Therefore, we have;

The speed rate of the bus = 39 + x

Distance = Speed × Time

The distance Janet travels to the bus station = The speed with which Janet travels on her bike × The time Janette spends on her bike to get to bus station

The distance Janet travels to the bus station = x × 0.5 = 0.5·x

The distance travelled by the bus from the bus station to her work = The speed of the bus × The time Janette spends on the bus from the bus station to her place of work

∴The distance travelled by the bus from the bus station to her work = (39 + x) × 2/3 hours = 13 + 2/3·x

The total distance from her home to her work = 40 miles = The distance Janet travels to the bus station + The distance travelled by the bus from the bus station to her work

∴ The total distance from her home to her work = 40 miles = 0.5·x + 13 + 2/3·x

Which gives;

40 = 0.5·x + 13 + 2/3·x

40 = 7/6·x + 13

7/6·x = 40 - 13 = 27

7/6·x = 27

x = 27 × 6/7 ≈ 23.14 mph

The rate of the bike = x ≈ 23.14 mph

The rate of the bike ≈ 23.14 mph

The speed rate of the bus = 39 + x ≈ 39 + 23.14 ≈ 62.14 mph

The speed rate of the bus ≈ 62.14 mph.

5 0

3 years ago