Which number is the same distance from 0 on a number line as 3/2 answers -3 -3/2 -2/3 2/3 3

Data from the article "The Osteological Paradox: Problems inferring Prehistoric Health from Skeletal Samples" (Current Anthropol

iris [78.8K]

Answer:

(a) P (X < 109.78) = 0.9484.

(b) P (X < 109.78) = 0.9484.

(c) P (97 < X < 106) = 0.5328.

(d) P (X < 85.6 or X > 111.4) = 0.0369.

(e) P (X > 103) = 0.3085.

(f) P (X < 98.2) = 0.3821.

(g) P (100 < X < 124) = 0.5000.

(h) The middle 80% of all heights of 5 year old children fall between 92.31 and 107.70.

Step-by-step explanation:

It is provided that X follows a Normal distribution with mean, μ = 100 and standard deviation, σ = 6.

(a)

Compute the value of P (X > 89.2) as follows:

$P (X>89.2)=P(\frac{X-\mu}{\sigma}>\frac{89.2-100}{6})\\=P(Z>-1.80)\\=P(Z$

Thus, the value of P (X > 89.2) is 0.9641.

(b)

Compute the value of P (X < 109.78) as follows:

$P (X$

Thus, the value of P (X < 109.78) is 0.9484.

(c)

Compute the value of P (97 < X < 106) as follows;

P (97 < X < 106) = P (X < 106) - P (X < 97)

$=P(\frac{X-\mu}{\sigma}$

Thus, the value of P (97 < X < 106) is 0.5328.

(d)

Compute the value of P (X < 85.6 or X > 111.4) as follows;

P (X < 85.6 or X > 111.4) = P (X < 85.6) + P (X > 111.4)

$=P(\frac{X-\mu}{\sigma}\frac{111.4-100}{6})\\=P(Z1.9)\\=0.0082+0.0287\\=0.0369$

Thus, the value of P (X < 85.6 or X > 111.4) is 0.0369.

(e)

Compute the value of P (X > 103) as follows:

$P (X>103)=P(\frac{X-\mu}{\sigma}>\frac{103-100}{6})\\=P(Z>0.50)\\=14-P(Z$

Thus, the value of P (X > 103) is 0.3085.

(f)

Compute the value of P (X < 98.2) as follows:

$P (X$

Thus, the value of P (X < 98.2) is 0.3821.

(g)

Compute the value of P (100 < X < 124) as follows;

P (100< X < 124) = P (X < 124) - P (X < 100)

$=P(\frac{X-\mu}{\sigma}$

Thus, the value of P (100 < X < 124) is 0.5000.

(h)

Compute the value of x₁ and x₂ as follows if P (x₁ < X < x₂) = 0.80 as follows:

$P(X_{1}$

The value of z is ± 1.282.

The value of x₁ and x₂ are:

$-z=\frac{x_{1}-\mu}{\sigma} \\-1.282=\frac{x_{1}-100}{6}\\x_{1}=100-(6\times1.282)\\=92.308\\\approx92.31$ $z=\frac{x_{2}-\mu}{\sigma} \\1.282=\frac{x_{2}-100}{6}\\x_{2}=100+(6\times1.282)\\=107.692\\\approx107.70$

Thus, the middle 80% of all heights of 5 year old children fall between 92.31 and 107.70.

5 0

2 years ago

[ (-5) + (-4) ]x • (-5) - (-7)x + (-3)x

pantera1 [17]

Answer: 49x

Step-by-step explanation:

first, i rewrite the equation, removed the parentheses, and multiplied it all out.

(-5-4)x x (-5) + 7x - 3x

then, i calculated it.

-9x x (-5) + 7x - 3x

then, i multiplied and calculated again.

45x + 7x - 3x = 49x

3 0

2 years ago

On January 1st, Jerome concocts a rumor and tells Beth. On January 2nd, they each tell a new person. By the end of January 2nd,

Kamila [148]

The rumor is spreading to a double amount of people each time and started with only one person.
On the first day, two people knew it. 2¹ = 2
On the second day, four people knew it. 2² = 4
On the third day, eight people knew it. 2³ = 8
On the nth day, the people that will know it = 2ⁿ
Thus, on the eighth day: 2⁸ = 256 people will know it

5 0

3 years ago

Read 2 more answers

Mike and Joey bought identical loaves of bread and packages of bologna. Mike made sandwiches with 5 slices of bologna and had 4

Sedaia [141]

Answer:

Mike had 14 slice of bread in his loaf while

Joey had 8 slice of bread in his loaf.

Step-by-step explanation:

We should note that a sandwich is made up of two slice of bread.

that is :

A Sandwich = 2 Slice of bread

and for bologna to be in a sandwich, you will have 2 slice of bread together.

So, For Mike,

2 slice of bread × 5 Sandwich = 10 Slice of bread

Remaining Slice of bread = 4 Slice

Total Slice of bread in Mike loaf = 10 + 4

= 14 slice of bread was in Mike loaf of bread.

For Joey

A sandwich = 2 Slice of bread

2 slice of bread × 4 Sandwich = 8 Slice of bread

Remaining slice of bread = 0

Total slice of bread in joey loaf = 8 slice of bread.

8 0

3 years ago

Read 2 more answers

A biologist was interested in determining whether sunflower seedlings treated with and an extract from Vinca minor roots resulte

Aleksandr-060686 [28]

Answer:

Kindly check explanation

Step-by-step explanation:

H0 : μ = 15.7

H1 : μ < 15.7

This is a one sample t test :

Test statistic = (xbar - μ) ÷ (s/√(n))

n = sample size = 33

Using calculator :

The sample mean, xbar = 15.41

The sample standard deviation, s = 0.419

Test statistic = (15.41 - 15.70) ÷ (0.419/√(33))

Test statistic = - 3.976

Using the Pvalue calculator :

Degree of freedom, df = n - 1 ; 33 - 1 = 32

Pvalue(-3.976, 32) = 0.000187

Decison region :

Reject H0 if Pvalue < α

Since Pvalue < α ; we reject H0

There is significant evidence to conclude that the true average height of the seedlings treated with an extract from Vinca minor roots is less than 15.7 cm.

4 0

2 years ago