Ask question

Ask question

All categories

3 years ago

10

This is used for the next few questions: The rating for the new scary movie has a scale of 0 to 10. The average response was tha

t the regular movie attendant enjoyed the movie with 8.3 points and a standard deviation of 0.5 points. What is the percent of people who gave the movie a rating between 6.8 and 8.8? (Write the number as a percent only without a percent sign.)

1 answer:

Pie3 years ago

4 0

Answer:

The percentage that of people who gave the movie a rating between 6.8 and 8.8

<em>P(6.8≤X≤8.8) = 83.9≅ 84 percentage</em>

Step-by-step explanation:

<u> Step(i):-</u>

Mean of the Population = 8.3 points

Standard deviation of the Population = 0.5 points

Let 'X' be the random variable in normal distribution

<em>Let X = 6.8</em>

$Z = \frac{x-mean}{S.D} = \frac{6.8-8.3}{0.5} = -3$

Let X = 8.8

$Z = \frac{x-mean}{S.D} = \frac{8.8-8.3}{0.5} = 1$

The probability that of people who gave the movie a rating between 6.8 and 8.8

<em>P(6.8≤X≤8.8) = P(-3≤Z≤1)</em>

= P(Z≤1)- P(Z≤-3)

= 0.5 + A(1) - ( 0.5 -A(-3))

= A(1) + A(3) (∵A(-3)=A(3)

= 0.3413 +0.4986 (∵ From Normal table)

= 0.8399

<u><em>Conclusion:-</em></u>

The percentage that of people who gave the movie a rating between 6.8 and 8.8

<em>P(6.8≤X≤8.8) = 83.9≅ 84 percentage</em>

You might be interested in

A survey report states that 70% of adult women visit their doctors for a physical examination at least once in two years. If 20

irakobra [83]

Answer:

a) 0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.

b) 0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.

Step-by-step explanation:

For each women, there are only two possible outcomes. Either they visit their doctors for a physical examination at least once in two years, or they do not. The probability of a woman visiting their doctor at least once in this period is independent of any other women. This means that we use the binomial probability distribution to solve this question.

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.

70% of adult women visit their doctors for a physical examination at least once in two years.

This means that $p = 0.7$

20 adult women

This means that $n = 20$

(a) Fewer than 14 of them have had a physical examination in the past two years.

This is:

$P(X < 14) = 1 - P(X \geq 14)$

In which

$P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

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

$P(X = 14) = C_{20,14}.(0.7)^{14}.(0.3)^{6} = 0.1916$

$P(X = 15) = C_{20,15}.(0.7)^{15}.(0.3)^{5} = 0.1789$

$P(X = 16) = C_{20,16}.(0.7)^{16}.(0.3)^{4} = 0.1304$

$P(X = 17) = C_{20,14}.(0.7)^{17}.(0.3)^{3} = 0.0716$

$P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278$

$P(X = 19) = C_{20,19}.(0.7)^{19}.(0.3)^{1} = 0.0068$

$P(X = 20) = C_{20,20}.(0.7)^{20}.(0.3)^{0} = 0.0008$

So

$P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.6079$

$P(X < 14) = 1 - P(X \geq 14) = 1 - 0.6079 = 0.3921$

0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.

(b) At least 17 of them have had a physical examination in the past two years

$P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

From the values found in item (a).

$P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.107$

0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.

6 0

3 years ago

A triangle has a base of 4x-7 and a height of 2x + 3. Find the area.

wolverine [178]

Answer:

area = ‐11

Step-by-step explanation:

hope this is correct and helps

7 0

3 years ago

Which statements must be true? Select each correct answer.

Verdich [7]

The answer choices ? did u forgot that

8 0

3 years ago

Read 2 more answers

Chuck is taking his kids to the store to buy new Converse shoes. He is given a choice of high tops or low tops. They may choose

monitta

Answer:

the possible outcome are two but don't trust me on that

8 0

3 years ago

Can someone help me please?

marishachu [46]

(6x + 30)+(2x+6)= 180
8x +36= 180
8x= 144
X= 18
So 2x+6 = 42
And 6x+30 = 138

8 0

3 years ago