Mathematics, 08.03.2021 19:30 paulinahunl17

There are many regulations for catching lobsters off the coast of New England including required permits, allowable gear, and size prohibitions. The Massachusetts Division of Marine Fisheries requires a minimum carapace length measured from a rear eye socket to the center line of the body shell. For a particular local municipality, any lobster measuring less than 3.37 inches must be returned to the ocean. The mean carapace length of the lobsters is 4.01 inches with a standard deviation of 2.13 inches. A random sample of 60 lobsters is obtained. Required:
What is the probability that the sample mean carapace length is more than 4.25 inches?

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Answer from: mya1318

Probability that the sample mean carapace length is more than 4.25 inches = 0.9993

Step-by-step explanation:

Given - There are many regulations for catching lobsters off the coast

of New England including required permits, allowable gear, and

size prohibitions. The Massachusetts Division of Marine Fisheries

requires a minimum carapace length measured from a rear eye

socket to the center line of the body shell. For a particular local

municipality, any lobster measuring less than 3.37 inches must

be returned to the ocean. The mean carapace length of the

lobsters is 4.01 inches with a standard deviation of 2.13 inches.

A random sample of 60 lobsters is obtained.

To find - What is the probability that the sample mean carapace length

is more than 4.25 inches?

Proof -

Given that, μ = 4.01, σ = 2.13 , n = 60

Now,

μₓ⁻ = σ / √n

= $\frac{2.13}{\sqrt{60} }$

= $\frac{2.13}{7.746}$ = 0.275

⇒μₓ⁻ = 0.275

Now,

P(X⁻ > 3.37) = 1 - P( X⁻ < 3.37)

= 1 - P(z < $\frac{3.37 - 4.25}{0.275}$ )

= 1 - P( z < -3.2 )

= 1 - 0.0007

= 0.9993

⇒P(X⁻ > 3.37) = 0.9993

∴ we get

Probability that the sample mean carapace length is more than 4.25 inches = 0.9993

Answer from: Quest

One shot. if 60% of 10 is 6, then what is 70%? we know it would be seven (since 60% is mathematically 60/100, or 6/10, then 70% is 70/100, or 7/10) but we can check anyway using ratios: 6 : 60% = x : 70%*inverse multiplicationx * 60% = 6 * 70%*divide both sides by 60%x = (6 * 70%) / 60%x = 7and since he has made 6 shots already, he would need just one more to get 7 shots or 70%. if the explanation is too confusing, comment and i will try to

Answer from: Quest

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where, $a = \frac{\sum y \sum x^2 - \sum x\sum xy}{n\sum x^2 - (\sum x)^2}$

here given table is,

price ($), x : 18 23 25 29 30 33

pairs sold, y : 16 13 10 8 6 2

so, $\sum x = 158$ , $\sum y = 55$ , $\sum xy = 1315$ ,

$\sum x^2 = 4308$ and $\sum y^2 = 629$ ,

thus, slop of the given line is,

$a = \frac{55\times 4308-158\times 1315}{6\times 4308-(158)^2}$

⇒ $a = \frac{29170}{884}$

⇒ $a =32.9977375566$ ≈ 33

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