# In a recent survey it was found that Americans drink an average of 23.2 gallons of bottled water in a year. If the standard deviation is 2.7 gallons and the variable is normally distributed, find the probability that a randomly selected American drinks more than 25 gallons of bottled water in a year. What is the probability that the selected person drinks between 22 and 30 gallons

a) 0.25249

b) 0.66575

Step-by-step explanation:

We solve this question using z score formula

= z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 23.2 gallons

σ is the population standard deviation = 2.7 gallons

a) Find the probability that a randomly selected American drinks more than 25 gallons of bottled water in a year.

For x = 25 gallons

z = 25 - 23.2/2.7

z = 0.66667

Probability value from Z-Table:

P(x<25) = 0.74751

P(x>25) = 1 - P(x<25)

1 - 0.74751

= 0.25249

The probability that a randomly selected American drinks more than 25 gallons of bottled water in a year is 0.25249

2) What is the probability that the selected person drinks between 22 and 30 gallons

For x = 22 gallons

z = 22 - 23.2/2.7

z = -0.44444

Probability value from Z-Table:

P(x = 22) = 0.32836

For x = 30 gallons

z = 30 - 23.2/2.7

z =2.51852

Probability value from Z-Table:

P(x = 30) = 0.99411

The probability that the selected person drinks between 22 and 30 gallons is

P(x = 30) - P(x = 22)

= 0.99411 - 0.32836

= 0.66575

The probability that a randomly selected American drinks more than 25 gallons of bottled water in a year is approximately 0.2514, while the probability that they will drink between 22 and 30 gallons is approximately 0.6643.

### Explanation:

This is a statistics question about probability distribution, specifically, normal distribution. You need to find the z-scores and use the standard normal distribution table to find the probabilities.

The average or mean (μ) consumption is 23.2 gallons and standard deviation (σ) is 2.7 gallons.

First, we use the z-score formula: z = (X - μ) / σ

To find out the probability that a selected American drinks more than 25 gallons annually, we substitute X = 25, μ = 23.2 and σ = 2.7 into the z-score formula to get z = (25 - 23.2) / 2.7 ≈ 0.67. Z value of 0.67 corresponds to the probability of 0.7486 in standard normal distribution table, but this is the opposite of what we want. We need to subtract this probability from 1 to find the probability that a person drinks more than 25 gallons annually. So 1 - 0.7486 = 0.2514.

Second, to find the probability an individual drinks between 22 and 30 gallons, we calculate two z-scores: For X = 22, z = (22 - 23.2) / 2.7 ≈ -0.44 with corresponding probability 0.3300, and for X = 30, z = (30 - 23.2) / 2.7 ≈ 2.52 with corresponding probability 0.9943. We find the probability of someone drinking between these quantities by subtracting the smaller probability from the larger, 0.9943 - 0.3300 = 0.6643.

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## Related Questions

A world class sprinter ran 200 m in 22.75s. What was her average speed?m/s
Enter a number.

8.8

Step-by-step explanation:

speed=distance/time

speed- ?

distance- 200m

time- 22.75s

?=200/22.75

?= 8.791...

round it so that it becomes 8.8

The circumference of a circle is22 cm find the radiusof the circle​

3.5cm

Step-by-step explanation:

8.A recipe calls for 4 cups of dry ingredients. Of the 4 cups, 1 cup
is flour. What is the ratio of cups of flour to cups of
other dry ingredients used in the recipe? write as a fraction

I think the answer here is 1/3.

1 being the cup of flour and 3 are the remaining cups of other ingredients.

Use​ Gauss's approach to find the following sum​ (do not use​ formulas):5+11+17+23...+83

Denote the sum by S. So

S = 5 + 11 + 17 + 23 + ... + 83

There's a constant difference of 6 between consecutive terms in S, so the 3 terms before 83 are 77, 71, and 65. So

S = 5 + 11 + 17 + 23 + ... + 65 + 71 + 77 + 83

Gauss's approach involves inverting the sum:

S = 83 + 77 + 71 + 65 + ... + 23 + 17 + 11 + 5

If we add terms in the same position in the sums, we get

2S = (5 + 83) + (11 + 77) + ... + (77 + 11) + (83 + 5)

and we notice that each grouped term on the right gives a total of 88. So the right side consists of several copies n of 88, which means

2S = 88n

and dividing both sides by 2 gives

S = 44n

Now it's a matter of determining how many copies get added. The terms in the sum form an arithmetic progression that follows the pattern

11 = 5 + 6

17 = 5 + 2*6

23 = 5 + 3*6

and so on, up to

83 = 5 + 13*6

so n = 13, which means the sum is S = 44*13 = 572.

To find the sum of the given arithmetic series, we can use Gauss's approach by finding the number of terms and then calculating the sum using the formula for the sum of an arithmetic series.

### Explanation:

To find the sum of the given series, we can use Gauss's approach. The series is an arithmetic progression with a common difference of 6. We can find the number of terms in the series using the formula for the nth term of an arithmetic sequence and then use the formula for the sum of an arithmetic series to find the sum.

1. Find the number of terms (n):
1. The first term (a) is 5, and the common difference (d) is 6.
2. Find the last term (l) using the formula: l = a + (n - 1)d
3. Substitute the values and solve for n: 83 = 5 + (n - 1)6
4. Simplify and solve for n: n = 15
2. Find the sum (S):
1. The formula for the sum of an arithmetic series is: S = (n/2)(a + l)
2. Substitute the values and solve for S: S = (15/2)(5 + 83)
3. Calculate the sum: S = 15(44)
4. Simplify the sum: S = 660

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2.) What amount presently must be invested earning 5.25% compounded continuouslyso that it will grow up to be worth $25,000 12 years from now? ### Answers The amount A resulting from a principal amount P being invested at rate r compounded continuously for time t is given by ... A = P·e^(rt) FIll in your given values and solve for P. ... 25000 = P·e^(0.0525·12) = P·e^0.63 ... P = 25000/e^0.63 ≈ 13314.80 . . . . . divide by the coefficient of P The amount that must be invested is$13,314.80.

An initial investment (P) compounded continuously with a rate of interest (r) in time (t) will grow to amount (Q) is given by:

Q = P * e^(rt)

Q=25000, r=0.0525, t=12

25000 = P * e^(0.0525*12)

1.8776P = 25000

P = 13314.8

Which number(s) below belong to the solution set of the inequality? Check all that apply. 9x 117A.
12

B.
14

C.
19

D.
13

E.
6

F.
8