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Leya [2.2K]
3 years ago
6

The st. joe company grows pine trees and the average annual increase in tree diameter is 3.1 inches with a standard deviation of

0.5 inch. a random sample of n = 50 trees is collected. what is the probability of the sample mean being less the 2.9 inches?
Mathematics
1 answer:
77julia77 [94]3 years ago
5 0

Solution: We are given:

μ=3.1,σ=0.5,n=50

We have to find P(Mean <2.9)

We need to first find the z score

z= (xbar-μ)/(σ/sqrt(n))

=(2.9-3.1)/(0.5/sqrt(50))

=(-0.2)/0.0707

=-2.83

Now we have to find P(z<-2.83)

Using the standard normal table, we have:

P(z<-2.83)=0.0023

Therefore the probability of the sample mean being less the 2.9 inches is 0.0023

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Use the numbers 2,3,5 and 8 to write an expression that has a value of -1. You may use any operations, and you must use each of
MaRussiya [10]
(5 * 2) - (8 + 3) = 10 - 11 = -1
7 0
3 years ago
Read 2 more answers
A study showed that 25% of the students drive themselves to school. Based on the suggested probability, in a class of 18 student
Gwar [14]

Answer:

B) 0.283

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

25% of the students drive themselves to school.

This means that p = 0.25

Class of 18 students

This means that n = 18

What would be the probability that at least 6 students drive themselves to school?

This is

P(X \geq 6) = 1 - P(X < 6)

In which

P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{18} = 0.006

P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{17} = 0.034

P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{16} = 0.096

P(X = 3) = C_{15,3}.(0.25)^{3}.(0.75)^{15} = 0.17

P(X = 4) = C_{15,4}.(0.25)^{4}.(0.75)^{14} = 0.213

P(X = 5) = C_{15,5}.(0.25)^{5}.(0.75)^{13} = 0.199

P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.006 + 0.034 + 0.096 + 0.17 + 0.213 + 0.199 = 0.718

P(X \geq 6) = 1 - P(X < 6) = 1 - 0.718 = 0.282

Closest option is B, just a small rounding difference.

4 0
3 years ago
ALGEBRA 1 HELP!! Andrea buys 4 bags of granola and 3 bags of dried fruit. She spends $51.50. Carter buys 2 bags of granola and 4
timurjin [86]

Answer:

Granola is $6.95/bag and Dried Fruit is $7.90/bag.

Step-by-step explanation:

Let G and F stand for the cost of 1 bag Granola and 1 bag dried Fruit.

We learn that Andrea's total was $51.50.  Her purchase can be written as the sum of the cost of 4 bags granola (4G) and 3 bags fruit (3F):

   4G + 3F = $51.50

We can do the same for Carter:

   2G + 4F = $45.50

We have two equations and two unknowns, so we should be able to solve for both unknowns.  To do this, we need to find a way to eliminate one of the unknows in a single equation.  Let's rearrange Carter's equation to isolate G on one side:

2G + 4F = $45.50

2G  = $45.50 - 4F

G = ($45.50 - 4F)/2

Now use this expression for G in Andrea's equation:

4G + 3F = $51.50

4(($45.50 - 4F)/2) + 3F = $51.50

2($45.50 - 4F) + 3F = $51.50

($91.00 - 8F) + 3F = $51.50

-5F = - $39.5

F = $7.90  <u>One bag of dried fruit is $7.90.</u>

Now use this value for F in either equation for find G:

2G  = $45.50 - 4F

2G  = $45.50 - 4($7.90)

2G = $13.90

G = $6.95   <u>One bag of granola is $6.95</u>

---------------

Check to see if these values work:

<u>Andrea: </u>

4G + 3F = $51.50  :

4($6.95) + 3($7.90) = $51.50  ?

$51.50 = $51.50   <u>YES</u>

<u>Carter:</u>

2G + 4F = $45.50

2($6.95) + 4($7.90) = $45.50  ?

$45.50                     =  $45.50   <u>YES</u>

<u></u>

4 0
3 years ago
Find the measure of ∠5.<br><br> Given:<br> ∠4 = 37°<br> ∠8 = 62°
Lisa [10]

Answer:

99

Step-by-step explanation:

Geometry is not my best subject but here's what I did:

The sum of the angles in a triangle is 180 so if we add 4 and 8 we can get angle 6

--> 180 - (37+62)

--> 180 - 99

---> 81

The sum of the angles on a line intersected at a point = 180

180 - 81 = Angle 5

Angle 5 = 99

5 0
3 years ago
I’m stuck please help me
gulaghasi [49]

Answer:

7

Step-by-step explanation:

→ First find the hypotenuse of length 2 and 3

√2² + 3² = √13

→ Use it to find the length of d

√6² + (√13)² = 7

4 0
3 years ago
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