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maria [59]
3 years ago
8

The mean incubation time of fertilized eggs is 21 days. Suppose the incubation times are approximately normally distributed with

a standard deviation of 1 day.(a) Determine the 20th percentile for incubation times.(b) Determine the incubation times that make up the middle 39% of fertilized eggs.
Mathematics
1 answer:
Korvikt [17]3 years ago
4 0

Answer:

a) 20.16; b) 20.49 and 21.51

Step-by-step explanation:

We use z scores for each of these.  The formula for a z score is

z=\frac{X-\mu}{\sigma}.

For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.

Using this, 21 as the mean and 1 as the standard deviation,

-0.84 = (X-21)/1

-0.84 = X-21

Add 21 to each side:

-0.84+21 = X-21+21

20.16 = X

For part b, we want the middle 39%.  This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want

50-19.5 = 30.5% = 0.305 and

50+19.5 = 69.5% = 0.695.

Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:

-0.51 = (X-21)/1

-0.51 = X-21

Add 21 to each side:

-0.51+21 = X-21+21

20.49 = X

0.51 = (X-21)/1

0.51 = X-21

Add 21 to each side:

0.51+21 = X-21+21

21.51 = X

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AlladinOne [14]

Answer:

52degrees

Step-by-step explanation:

Let the measure of the largest angle be x

middle angle be y

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Since the sum of angle in a triangle is 180 degrees, hence;

x + y + z = 180 .... 1

If the measure of the largest angle is 32 less than 3 times the smallest angle, then;

x = 3z - 32

3z = x+ 32

z = x+32/3 ..... 2

If he measure of the middle angle is 8 more than half the measure of the largest angle, then;

y = x/2 + 8 .... 3

Substitute 2 and 3 into 1;

x + x/2 + 8 + (x+32)/3 = 180

multiply through by 6

6x + 3x + 48 + 2(x+32) = 1080

9x + 48 + 2x + 64 = 1080

11x + 112 = 1080

11x = 1080-112

11x = 968

x = 968/11

x = 88 degrees

Get the middle angle y;

Since y = x/2 + 8

y = 88/2 + 8

y = 44 + 8

y = 52 degrees

Hence the measure of the middle angle is 52degrees

5 0
3 years ago
dillon pays x dollars to get a haircut. he gives the stylist a 15% tip. the expression representing his total cost is x + 0.15x
bagirrra123 [75]

Answer:

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Step-by-step explanation:

Given expression = x + 15% of x

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Step-by-step explanation:

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mezya [45]
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7 0
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butalik [34]

Answer:

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