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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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Which of the following will make a confidence interval narrower and more precise?
swat32

Answer:

B. Larger sample size and lower confidence level

Step-by-step explanation:

The margin of error of a confidence interval is given by the following formula:

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

z is related to the confidence level. The higher the confidence level, the higher the value of Z.

So, the margin of error is direct proportion to the confidence level and inverse proportional to the sample size.

We want to decrease the margin of error.

So the correct answer is:

B. Larger sample size and lower confidence level

6 0
3 years ago
If x equals 12, find the value of x2​
eduard

Answer:

24

Step-by-step explanation:

12 * 2 = 24

7 0
3 years ago
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Camilla makes and sells Jewelry. She has 8,160 silver beads and 2,880 black beads to make a necklace. Each necklace will contain
Svetlanka [38]

Answer:

96.

Step-by-step explanation:

Divide the silver beads by 85=96

Then divide the black beads by 30=96.

Total necklaces that can be made: 96

4 0
2 years ago
WHAT VALUE IS EQUIVALENT TO (7+3)^2 + (8-1) X 5 EQUAL
sdas [7]

Answer:

135

Step-by-step explanation:

(7+3)^2 + (8-1) * 5

Parentheses first

(10)^2 + (7) * 5

Exponents next

100 + 7*5

Multiply

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Add

135

7 0
2 years ago
How many 4 digit multiples can not be divided by 5
Advocard [28]

Answer:

1800

Step-by-step explanation:

Let us solve this question by Modular Airthmatic.

Let the lowest 4 digit number be X.

X= 1 (mod 5)

X =2 (mod 5)

X=3 (mod 5)

X =4 (mod 5)

X=1+5 t where t is any integer.

1+5 t=2 (mod 5)

5 t=1 (mod 5 )

5 is the Modular Inverse of modulo 5

t=1 (mod 5)

t =1+5 u : u= any integer.

X becomes 1+ 5 (1+5u )=6+25 u

6+25u =3 (mod 5)

25 u= -3 (mod 5)=2 (mod 5)

25 is Modular Inverse of Modulo 5

u=2 (mod 5)

u =2+5 v : v= any integer.

X becomes 6 +25 (2+5 v)=56+125 v .

56 +125 v=4 (mod 5)

125 v=-52 (mod 5)=3 (mod 5)

125 is Modular Inverse of modulo 5

v = 3 (mod 5)

v =3 +5 w where w is any integer.

For lowest 4 digit number, take

w=200

X=1003 : Lowest 4 digit number.

Take w=201

X=208 : Next number.

For 4 digit largest number, take

w=1995

X= 9978 : Largest number.

No. of Numbers =(1995 - 200 )+1=1800 □Ans.

8 0
3 years ago
Read 2 more answers
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