How do i solve this ?

A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measurin

Ratling [72]

Answer:

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

Step-by-step explanation:

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

Can anyone help with expanding this?

igomit [66]

Answer:

log(4) +3 log(x) +7 log(y)

Step-by-step explanation:

Hope it helps!

7 0

3 years ago

Read 2 more answers

4(3x+2)−7x simplified

baherus [9]

Answer:

19x+8

Step-by-step explanation:

1) distribute the term outside the parenthesis to each term inside:

4*3x=12x

4*2=8

12x+8-7x

2) 12x+7x=19x

19x+8

Hope this helps!

7 0

3 years ago

The mass of the eggs laid by a certain breed of hen is a normally distributed random variable with mean 0.06kg and standard devi

Olin [163]

a (i) The number of standard size is 288 eggs

a (ii) The number of medium size is 1,476 eggs

a (iii) The number of large size is 36 eggs

b (i) The expected profit made from selling the standard size is Gh¢43.2

b (ii) The expected profit made from selling the medium size is Gh¢516.6

b (iii) The expected profit made from selling the large size is Gh¢16.2

The given parameters:

the mean of the distribution, m = 0.06 kg

standard deviation (std) of the distribution, d = 0.009 kg

number of the samples, n = 1800 eggs

(i) Find the position of "less than 0.052 kg (standard size)":

1 standard deviation below the mean = m - d

m - d = 0.06 kg - 0.009 kg = 0.051 kg

(the standard size is 1 standard deviation below the mean)

less than 1 standard deviation below the mean in a normal distribution is equal to 16% of the data samples

Number of standard size = 0.16 x 1800 = 288 eggs

(ii) Find the position of "Between 0.052 kg and 0.075kg (medium size)":

0.052 kg is 1 standard deviation below the mean

2 standard deviation above the mean = m + 2d
m + 2d = 0.06 + 2(0.009) = 0.078 kg

(the medium size is between 1 std below the mean and 2 std above the mean)

Between 1 std below the mean and 2 std above the mean in a normal distribution = (68 + 14)% = 82%

Number of medium size = 0.82 x 1800 = 1,476 eggs

(iii) Find the position of "Greater than 0.075 kg (large size)":

0.078 kg is 2 standard deviation below the mean
greater than 2 std above the mean in a normal distribution = 2 % of the data samples
Number of large size = 0.02 x 1800 = 36 eggs

Check: 288 eggs + 1476 eggs + 36 eggs = 1,800 eggs

(b) the cost of production of an egg = Gh¢0.45

the selling price of the standard size = Gh¢0.60

the selling price of the medium size = Gh¢0.80

the selling price of the large size = Gh¢0.95

(i) The expected profit made from selling the standard size:

Profit = total revenue - cost of production

Profit = 288(0.6) - 288(0.45) = Gh¢43.2

(ii) The expected profit made from selling the medium size:

Profit = total revenue - cost of production

Profit = 1476(0.8) - 1476(0.45) = Gh¢516.6

(iii) The expected profit made from selling the large size:

Profit = total revenue - cost of production

Profit = 36(0.9) - 36(0.45) = Gh¢16.2

Learn more here: brainly.com/question/22520030

3 0

3 years ago

Directive y=10, vertex=(-2,7)

Katyanochek1 [597]

1/34 bro trust okay bro

8 0

2 years ago