Rae and Doris are training to swim a 200-meter freestyle race. The table lists their practice times during training camp.

Forty percent of households say they would feel secure if they had $50,000 in savings. you randomly select 8 households and ask

Kay [80]

Answer:

Let X be the event of feeling secure after saving $50,000,

Given,

The probability of feeling secure after saving $50,000, p = 40 % = 0.4,

So, the probability of not feeling secure after saving $50,000, q = 1 - p = 0.6,

Since, the binomial distribution formula,

$P(x=r)=^nC_r p^r q^{n-r}$

Where, $^nC_r=\frac{n!}{r!(n-r)!}$

If 8 households choose randomly,

That is, n = 8

(a) the probability of the number that say they would feel secure is exactly 5

$P(X=5)=^8C_5 (0.4)^5 (0.6)^{8-5}$

$=56(0.4)^5 (0.6)^3$

$=0.12386304$

(b) the probability of the number that say they would feel secure is more than five

$P(X>5) = P(X=6)+ P(X=7) + P(X=8)$

$=^8C_6 (0.4)^6 (0.6)^{8-6}+^8C_7 (0.4)^7 (0.6)^{8-7}+^8C_8 (0.4)^8 (0.6)^{8-8}$

$=28(0.4)^6 (0.6)^2 +8(0.4)^7(0.6)+(0.4)^8$

$=0.04980736$

(c) the probability of the number that say they would feel secure is at most five

$P(X\leq 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)$

$=^8C_0 (0.4)^0(0.6)^{8-0}+^8C_1(0.4)^1(0.6)^{8-1}+^8C_2 (0.4)^2 (0.6)^{8-2}+8C_3 (0.4)^3 (0.6)^{8-3}+8C_4 (0.4)^4 (0.6)^{8-4}+8C_5(0.4)^5 (0.6)^{8-5}$

$=0.6^8+8(0.4)(0.6)^7+28(0.4)^2(0.6)^6+56(0.4)^3(0.6)^5+70(0.4)^4(0.6)^4+56(0.4)^5(0.6)^3$

$=0.95019264$

8 0

3 years ago

A middle school counselor randomly sampled students about their favorite subjects. Suppose an 8th grade student from the school

NISA [10]

Answer: B

Step-by-step explanation:

68 divided by 204 gives you 0.33 so round to nearest tenth and and go to 0.31 and then convert to percent and you have 31%

7 0

3 years ago

Find the value of x.

Gelneren [198K]

Answer: x=13

Step-by-step explanation:

5 0

2 years ago

Name : Teacher: Word Problems Score: Date : Tom has 24 blue balloons. He wants to give his six friends the same number of blue b

Karo-lina-s [1.5K]

Each friend of Tommy will receive 4 blue balloons from tommy as Tommy wants to distribute his balloons equally among all of them.

As per the question statement, Tom has 24 blue balloons and he wants to distribute his balloons equally among all 6 of his friends.

To solve this question, let us assume that each friend of Tommy received "x" balloons on equal distribution.

We will now form a Linear Equation of single variable with "x", based on the condition mentioned in the question statement, and solving for "x", we will obtain our desired answer, i.e.,

$(x+x+x+x+x+x)=24\\or, (6*x)=24\\or, x=\frac{24}{6}\\ or, x=4$

Thus, Each friend of Tommy will receive 4 blue balloons.

Linear Equation: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and hence comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c) where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.

Variable: In Mathematics, a variable is a symbol or a representative of a value, which is unknown.

To learn more about Linear Equations, click on the link below.

brainly.com/question/27664510

#SPJ9

3 0

1 year ago

On the scale drawing of a car, the length from bumper to bumper is 6 inches. The car"s actual length, from bumper to bumper, is

I am Lyosha [343]

Cross multiply and solve for x

6 0

3 years ago