Avery owns a small business selling bagels. She knows that in the last week 6

53% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the

faltersainse [42]

Answer:

a

$P(X = 5) = 0.2423$

b

$P( X \ge 6 )= 0.4516$

c

$P( X < 4 )= 0.12694$

Step-by-step explanation:

From the question we are told that

The population proportion is p = 0.53

The sample size is n = 10

Generally the distribution of the confidence of US adults in newspapers follows a binomial distribution

i.e

$X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial distribution is

$P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}$

Here C stands for combination hence we are going to be making use of the combination function in our calculators

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is exactly five is mathematically represented as

$P(X = 5) = ^{10}C_5 * 0.53^5 * (1- 0.53)^{10-5}$

=> $P(X = 5) = 252 * 0.04182 * 0.023$

=> $P(X = 5) = 0.2423$

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is at least six is mathematically represented as

$P( X \ge 6 )= P( X = 6) + P( X = 7) + P( X = 8) + P( X = 9) + P( X = 10)$

=> $P( X \ge 6 )= [^{10}C_6 * [0.53]^6 * (1- 0.53)^{10-6}] + [^{10}C_7 * [0.53]^7 * (1- 0.53)^{10-7}] + [^{10}C_8 * [0.53]^8 * (1- 0.53)^{10-8}] + [^{10}C_9 * [0.53]^9 * (1- 0.53)^{10-9}] + [^{10}C_{10} * [0.53]^{10} * (1- 0.53)^{10-10}]$

=> $P( X \ge 6 )= [0.227] + [0.1464] + [0.0619] + [0.0155] + [0.00082]$

=> $P( X \ge 6 )= 0.4516$

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is less than four is mathematically represented as

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

=> $P( X < 4 )= [^{10}C_3 * 0.53^3 * (1- 0.53)^{10-3}] + [^{10}C_2 * 0.53^2 * (1- 0.53)^{10-2}] + [^{10}C_1 * 0.53^1 * (1- 0.53)^{10-1}] + [^{10}C_0 * 0.53^0 * (1- 0.53)^{10-0}]$

=> $P( X < 4 )= 0.09051 + 0.03 + 0.0059 + 0.000526$

=> $P( X < 4 )= 0.12694$

5 0

2 years ago

1. The scale of a map is 1 in = 19.5 mi map: ________ in actual: 9.5 mi 2. The scale of a map is 7 in = 16 mi map: 4.9 in actual

alexandr402 [8]

We use ratio and proportion to solve each of these:

1. The scale of a map is 1 in = 19.5 mi map: ________ in actual: 9.5 mi
1 in / 19.5 mi = x in / 9.5 mi, x = 0.487 in

2. The scale of a map is 7 in = 16 mi map: 4.9 in actual: ______ mi
7 in / 16 mi = 4.9 in / x mi, x = 11.2 mi

3. The scale factor for a model is 5 cm = ________ m Model : 72.5 cm actual: 165.3 m
5 cm / x m = 72.5 cm / 165.3 m, x = 11.4 m

4. The scale of a map is 1 in = 9.6 mi map: ________ in actual: 34.7 mi
1 in / 9.6 mi = x in / 34.7 mi, x = 3.62 in

5. The scale of a map is 1 ft = 9.6 mi map: ________ ft actual: 38.4 mi
1 ft / 9.6 mi = x ft / 38.4 mi, x = 4 ft

6. The scale factor for a model is 5 cm = ________ m Model : 22.4 cm actual: 155.2 m
5 cm / x m = 22.4 cm / 155.2 m, x = 34.64 m

7. The scale of a map is 5 in = 10 mi map: 8.7 in actual: ______ mi
5 in / 10 mi = 8.7 in / x mi, x = 17.4 mi

8. The scale of a map is 1 in = 13.5 mi map: ________ in actual: 65.9 mi
1 in / 13.5 mi = x in / 65.9 mi, x = 4.88 in

9. The scale factor for a model is 5 cm = ________ m Model : 61.5 cm actual: 143.2 m
5 cm / x m = 61.5 / 143.2 m, x = 11.64 m

10. The scale factor for a model is 5 cm = ________ m Model : 29.7 cm actual: 179.5 m
5 cm / x m = 29.7 cm / 179.5 m, x = 30.22 m

3 0

3 years ago

20 years ago, father's age was 5 times his son's age. Now his age is 10 years more than twice his son's present age. Find their

Montano1993 [528]

Step-by-step explanation:

x = father's age now

y = son's age now

x = 2y + 10

x - 20 = 5(y - 20) = 5y - 100

using the first in the second equation :

2y + 10 - 20 = 5y - 100

-10 = 3y - 100

90 = 3y

y = 30

x = 2y + 10 = 2×30 + 10 = 60 + 10 = 70

the father is now 70 years old, the son now 30 years old.

6 0

1 year ago

A store uses the expression -2p+ 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere

Ivan

Answer:

B: $12.00 per backpack gives the maximum revenue; the maximum revenue is $312.00.

Step-by-step explanation:

3 0

2 years ago

Need help loveliesss

tiny-mole [99]

P=44.6

P=a+b+√a^2+b^2=11+15+√11^2+15^2≈44.6

3 0

2 years ago