Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.

To find : What is the approximate standard deviation of weight for this species of cockroaches?

Solution :

We have given,

Mean $\mu=50$

The sample mean x=55

A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.

i.e. P(X>55)=14%=0.14

The total probability needs to sum up to 1,

$P(X\leq 55)=1-P(X>55)$

$P(X\leq 55)=1-0.14$

$P(X\leq 55)=0.86$

The z-score value of 0.86 using z-score table is z=1.08.

Applying z-score formula,

$z=\frac{x-\mu}{\sigma}$

Where, $\sigma$ is standard deviation

Substitute the values,

$z=\frac{x-\mu}{\sigma}$

$1.08=\frac{55-50}{\sigma}$

$1.08=\frac{5}{\sigma}$

$\sigma=\frac{5}{1.08}$

$\sigma=4.62$

The standard deviation of weight for this species of cockroaches is 4.62.

4 0

3 years ago

How to decompose a parallelogram and rearrange the parts to form a rectangle is.

lukranit [14]

Answer:

a parrellelogram is a rectangle T^T

just that they slanted it.

UNSLANT IT.

if that makes sense.

3 0

2 years ago

if i supposedly got 2 cats and trained them to bring me quarters and they did and supposedly everyday i got 10 quarters how much

ivanzaharov [21]

Answer:

After a year you would have $1,825

Step-by-step explanation:

Amount for one cat a day in cents

10x25=250

Amount for one cat for a year in cents

250x365=91,250

Amount for both cats for a year in cents

91,250x2=182,500

Amount for both cats for a year dollars

182,500/100=1,825

8 0

1 year ago

The freezing point of water is 32º F. Tim added potassium and found

HACTEHA [7]

Answer:

The freezing point of the water with the added potassium is 24 degrees Fahrenheit.

Step-by-step explanation:

To find the freezing point of the water with the added potassium, you need to subtract 8 degrees from the initial freezing point of water, This is because you know that after adding potassium to water, the freezing point went down by 8 degrees Fahrenheit. So you need to subtract 8 degrees from the initial freezing point of water (32 degrees Fahrenheit). 32º F - 8º = 24º F. So the freezing point of the water with the added potassium is 24 degrees Fahrenheit.

5 0

2 years ago