An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.90 ounces and a standard deviation of 0.20 ounce. Suppose that you select a sample of 25 oranges. a. What is the probability that the sample mean amount of juice will be at least 4.85 ounces? b. The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean? c. The probability is 71% that the sample mean amount of juice will be greater than what value? a. The probability is nothing.

Step-by-step explanation:

Since the amount of juice squeezed from these oranges is approximately normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ/√n

Where

x = amount of juice squeezed.

µ = mean amount

σ = standard deviation

n = number of samples

From the information given,

µ = 4.90 ounces

σ = 0.20 ounce

n = 25

a) the probability that the sample mean amount of juice will be at least 4.85 ounces is expressed as

P(x ≥ 4.85) = 1 - P(x < 4.85)

For x = 4.85,

z = (4.85 - 4.9)/(0.2/√25) =

- 0.05/0.04 = - 1.25

Looking at the normal distribution table, the probability corresponding to the z score is 0.11

P(x ≥ 4.85) = 1 - 0.11 = 0.89

b) 70% = 70/100 = 0.7

Looking at the table, the two z scores corresponding to the probability value of 0.7 are 0.53 and - 0.53

For z = - 0.53,

- 0.53 = (x - 4.9)/(0.2/√25)

- 0.53 = (x - 4.9)/0.04

x - 4.9 = 0.04 × - 0.53 = - 0.0212

x = - 0.0212 + 4.9 = 4.88

For z = 0.53,

0.53 = (x - 4.9)/(0.2/√25)

0.53 = (x - 4.9)/0.04

x - 4.9 = 0.04 × 0.53 = 0.0212

x = 0.0212 + 4.9 = 4.92

c) P(x < 4.9)

The probability value is 71/100 = 0.71. Since the mean is greater, the probability value would be 1 - 0.71 = 0.29. Looking at the table, the z score corresponding to the probability value of 0.29 is - 0.55

Therefore,

- 0.55 = (x - 4.9)/(0.2/√25)

0.55 = (x - 4.9)/0.04

x - 4.9 = 0.04 × 0.55 = 0.022

x = 0.022 + 4.9 = 4.922

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!