Question

ANSWER QUICKLY PLEASE 2. Molecules in the air are moving with speeds based on the normal model.

Answer 1

Answer:

(a). The mean speed is 760 m/s.

(b). The standard deviation for our normal model is 142.1 m/s.

(c). The unusual speed is 1127 m/s.

(d). The average molecule speed is 929.48 m/s.

Step-by-step explanation:

Given that,

Molecules in the air are moving with speeds based on the normal model.

Let x be the speed of the molecules.

(a). If half of the air molecules are moving faster than 760 m/s.

We can say speed of a molecules is normally distributed.

So, the mean, median and mode of this distribution is at least greater than 760 m/s.

(b). If exactly 95% of the molecules are moving with speeds between 475.8 m/s and 1044.2 m/s,

If the standard deviation is σ and the mean is μ,

We need to calculate the standard deviation for our normal model

Using empirical rule

$\mu-2\sigma=475.8$...(I)

$\mu+2\sigma=1044.2$....(II)

Put the value of μ in equation (I)

$760-2\sigma=475.8$

$-\sigma=\dfrac{475.8-760}{2}$

$\sigma=142.1\ m/s$

(c). One molecule is found to be moving with a speed of 1127 m/s.

We know that,

1127 is the between 1126 and 1128.

Since, it is a continuous distribution,

We need to find the probability that speed is between this

Using excel function

$P(1126$

$P(1126$

We know that,

Any probability less than 0.05 is considered as unusual

So, 0.0002<0.05

So, 1127 will be considered as the unusual speed.

(d). If the temperature increase caused the z-score of a particle moving at 1100 m/s particle to drop to 1.2 after the temperature increase.

We need to calculate the average molecule speed

Using formula of average molecule speed

$z=\dfrac{x-\mu'}{\sigma}$

$-\mu'=z\sigma-x$

Put the value in to the formula

$-\mu'=1.2\times142.1-1100$

$\mu'=929.48\ m/s$

Hence, (a). The mean speed is 760 m/s.

(b). The standard deviation for our normal model is 142.1 m/s.

(c). The unusual speed is 1127 m/s.

(d). The average molecule speed is 929.48 m/s.