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Rashid [163]
3 years ago
6

Laboratory experiment shows that the life of the average butterfly is normally distributed with a mean of 18.8 days and a standa

rd deviation of 2 days.
Find the probability that a butterfly will live between 12.04 and 18.38 days.

a) 0.4164

b) 0.4203

c) 0.5828

d) 0.3893

e) 0.4202

f) None of the above.
Mathematics
1 answer:
inessss [21]3 years ago
6 0

Answer:

a) 0.4164

Step-by-step explanation:

Mean lifespan (μ) = 18.8 days

Standard deviation (σ) = 2 days

For any given lifespan 'X', the z-score is:

z=\frac{X- \mu}{\sigma} \\z=\frac{X- 18.8}{2}

For X=12.04 days:

z=\frac{12.04 - 18.8}{2} \\z=-3.38

A z-score of -3.38 falls in the 0.036-th percentile of a normal distribution.

For X=18.38 days:

z=\frac{18.38 - 18.8}{2} \\z=-0.21

A z-score of -3.38 falls in the 41.68th percentile of a normal distribution.

The probability that a butterfly lives between 12.04 and 18.38 days is

P=41.68-0.036\\P=41.64\%\ or\ 0.4164

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25

Step-by-step explanation:

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The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less
fomenos

Answer:

The answer to your question is below

Step-by-step explanation:

Equation 1

                            $sweatshirt = 2 pair of shorts

                                    <u>  w = 2h</u>

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Equation 3

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Step-by-step explanation:

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a rock is thrown from the top of a tall building. the distance, in feet, between the rock and the ground x seconds after it is t
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Answer:

1.5 seconds

Step-by-step explanation:

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0 = -16x² - 4x + 42 (Subtract 340 from both sides)

16x² + 4x - 42 = 0  (Multiply entire equation by -1, "flip" equation)

8x² + 2x - 21 = 0    (Divide entire equation by 2)

(4x + 7)(2x - 3) = 0  (Factor LHS)

4x + 7 = 0 or 2x - 3 = 0 (Zero Product Property)

4x = -7 or 2x = 3 (Subtract -7 and add 3 from/to both sides, respectively)

x = -\frac{7}{4} = -1.75 or  x =\frac{3}{2} = 1.5

x = -1.75 is an extraneous solution because in the context of the question, you can't have negative seconds so therefore, the final answer is 1.5 seconds.

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