IQ is normally distributed with a mean of 100 and a standard deviation of 15. What IQ do you need to be in the 90th percentile?

Answers

Answer 1

Answer:

Answer:IQ score≈119.7225

Step-by-step explanation:

To find the IQ score that corresponds to the 90th percentile in a normal distribution with a mean of 100 and a standard deviation of 15, you can use the cumulative distribution function (CDF) of the normal distribution. The CDF gives the probability that a random variable (in this case, IQ) is less than or equal to a specific value.

The formula to find the z-score (standard score) corresponding to a given percentile is:

�

invNorm

(

�

)

z=invNorm(p)

Where

�

p is the desired percentile expressed as a decimal (90th percentile would be

�

0.90

p=0.90), and

invNorm

invNorm is the inverse normal distribution function.

Then, you can use the z-score to find the IQ score using the formula:

IQ score

mean

�

standard deviation

IQ score=mean+z×standard deviation

Plugging in the given values:

Mean (

mean

mean) = 100

Standard deviation (

standard deviation

standard deviation) = 15

Percentile (

�

p) = 0.90

First, find the z-score:

�

invNorm

(

0.90

)

z=invNorm(0.90)

You can use a standard normal distribution table, calculator, or software to find the z-score. For a 90th percentile,

�

≈

1.28155

z≈1.28155.

Now, plug the z-score into the IQ score formula:

IQ score

100

1.28155

IQ score=100+1.28155×15

IQ score

≈

119.7225

IQ score≈119.7225

Rounding to the nearest whole number, an IQ score of approximately 120 would place you in the 90th percentile.

Answer 2

Answer:

Final answer:

To be in the 90th percentile, you would need an IQ score of approximately 119.2.

Explanation:

To find the IQ score corresponding to the 90th percentile, we can use the standard normal distribution table or a calculator. Since the IQ distribution is normally distributed with a mean of 100 and a standard deviation of 15, we can convert the given information into a standard normal distribution by using the formula:

Z = (X - μ) / σ

where Z is the standard score, X is the IQ score, μ is the mean, and σ is the standard deviation.

Since we want to find the IQ score for the 90th percentile, we need to find the Z-score that corresponds to the 90th percentile. From the standard normal distribution table, we find that the Z-score for the 90th percentile is approximately 1.28.

Now, we can solve for X (the IQ score) using the formula:

Z = (X - μ) / σ

Substituting the values, we have:

1.28 = (X - 100) / 15

Solving for X, we get:

X = 1.28 * 15 + 100

Therefore, to be in the 90th percentile, you would need an IQ score of approximately 119.2.

Learn more about calculating iq for a given percentile here:

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4 An alloy is a mixture of metals. Most of the gold used in jewellery is an alloy of pure gold and other metals which are added to make the gold harder. Pure gold is 24 carats (ct), so 18 carat parts pure gold 18 gold is an alloy of gold and other metals in the ratio 18:6. In other words, 18/24 parts pure gold and 6/24 other metals. a. A jeweller makes an 18 ct gold alloy using three grams of pure gold. What mass of other metals does she add?
b . An 18 ct gold chain contains four grams of pure gold. How much other metal does it contain? c. What is the ratio of gold to other metals in 14 ct gold?
d. What is the ratio of gold to other metals in 9 ct gold?

Answers

To calculate the mass of other metals in each scenario, we need to use the given ratios.

Given:

- Pure gold is 24 carats (ct).

- 18 carat gold is an alloy of gold and other metals in the ratio 18:6 (18/24 parts pure gold and 6/24 other metals).

a. A jeweller makes an 18 ct gold alloy using three grams of pure gold. What mass of other metals does she add?

First, let's find the mass of other metals in the 18 ct gold alloy.

18 ct gold contains 18/24 parts pure gold and 6/24 parts other metals. So, if the jeweller uses 3 grams of pure gold, the amount of other metals in the alloy can be calculated as follows:

Mass of other metals = (6/24) * 3 grams

Mass of other metals = (1/4) * 3 grams

Mass of other metals = 3/4 grams

b. An 18 ct gold chain contains four grams of pure gold. How much other metal does it contain?

Similarly, for the 18 ct gold chain containing 4 grams of pure gold:

Mass of other metals = (6/24) * 4 grams

Mass of other metals = (1/4) * 4 grams

Mass of other metals = 4/4 grams

Mass of other metals = 1 gram

c. What is the ratio of gold to other metals in 14 ct gold?

For 14 ct gold, the ratio of gold to other metals is 14:10 (since 14 + 10 = 24, and gold is 14 out of 24 parts, while other metals are 10 out of 24 parts).

d. What is the ratio of gold to other metals in 9 ct gold?

For 9 ct gold, the ratio of gold to other metals is 9:15 (since 9 + 15 = 24, and gold is 9 out of 24 parts, while other metals are 15 out of 24 parts).

An order for 50 units is processed on work centers A and B. The set up time on A is 45 Min and run time is 5 min per piece. The set up time on B is 30 Min and run time is 4 min per piece. Wait time between the two operations is 8 hours. The move time between A and B is 60 min. Wait time after B is 8 hours and the move time into stores is 2 hrs. Queue at work center A is 25 hours and at B is 35 hrs. Calculate the total manufacturing lead time for the order.

Answers

Answer:

5265 mins or 87.75 hours

Step-by-step explanation:

There is a large amount of data in this question so we will first process it and simplify it

Given

Order = 50 units

Operation A

Setup Time = 45 mins

Run Time = 5 min/unit * 50 = 250 mins

Wait Time (Between A&B) = 8 hours = 480 mins

Move Time (Between A&B) = 60 mins

Queue Time = 25 hours = 1500 mins

Operation B

Setup Time = 30 mins

Run Time = 4 min/unit * 50 = 200 mins

Wait Time (After B) = 8 hours = 480 mins

Move Time (To Stores) = 2 hours = 120 mins

Queue Time = 35 hours = 2100 mins

Lead time refers to how long it takes from when the order is place to when it is delivered, so to calculate the total manufacturing lead time we will add all the above times which is 5265 mins or 87.75 hours

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Answers

The segment addition postulate states that if B is between A and C then AB+BC=AC.

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Answers

Answer:

Total number of ways will be 20

Step-by-step explanation:

We have given three identical green shirts and three identical red shirts

So total number of shirts = 3+3 = 5

We have to distribute these shirts to 6 children so that each children got one shirt

Number of ways will be equal to $=(6!)/(3!3!)=20$ ( Here we divide by 3!3! because three green shirts and 3 red shirts are identical )

There are about 2.2 pounds in one kilogram. If Miguel's bag weighs37.4 kilograms, about how many pounds does it weigh? Did you multiply

or divide to find your answer? my last points help ASAP

Answers

Answer:

82.28

Step-by-step explanation:

1kg=2.2 pounds

$37.4 * 2.2 = 82.28$

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Answers

32 meters tall.
It would form a right triangle, in which the shorter leg is 7m and the longer leg is 24m. You're looking for the last side, the hypotenuse. So use the Pythagorean theorem. a^2 + b^2 = c^2 , in which a and b are the legs and c is the hypotenuse.
Therefore, you get 7^2 + 24^2 = c^2.
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Add, 625 = c^2.
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The broken part forms the hypotenuse of a right angled triangle.

So we have a right angled triangle, the vertical part is 7m, and the horizontal is 24m.

From Pythagoras' Theorem:

x² = 24² + 7²

x² = 576 + 49

x² = 625

x = √625

x = 25

So the broken part is 25m long.

The length of the flagpole before it was broken = 25 + 7

= 32m.

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