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shepuryov [24]
3 years ago
15

A gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than

work for someone else. A random sample of 600 18-29 year-olds is obtained today. What is the probability that no more than 70% would prefer to start their own business?
Mathematics
1 answer:
Neko [114]3 years ago
3 0

Answer:

The probability that no more than 70% would prefer to start their own business is 0.1423.

Step-by-step explanation:

We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.

Let \hat p = <u><em>sample proportion of people who prefer to start their own business</em></u>

The z-score probability distribution for the sample proportion is given by;

                               Z  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, p = population proportion who would prefer to start their own business = 72%

            n = sample of 18-29 year-olds = 600

Now, the probability that no more than 70% would prefer to start their own business is given by = P( \hat p \leq 70%)

       P( \hat p \leq 70%) = P( \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } \leq \frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } } ) = P(Z \leq -1.07) = 1 - P(Z < 1.07)

                                                                       = 1 - 0.8577 = <u>0.1423</u>

The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.

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Will a 7/32 inch diameter pin fit into a reamed hole with a diameter of 0.215 inches?
lana [24]

Answer:

no ... the pin will not fit the reamed hole

Step-by-step explanation:

The decimal equivalent of 7/32 is 0.21875.  This is larger than the reamed

hole:                                                  0.215

and so the answer is no ... the pin will not fit the reamed hole.

6 0
3 years ago
Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $28,000 over the next 6 year
Anna35 [415]

Given:

• Amount to save, A = $28,000

,

• Time, t = 6 years

,

• Interest rate, r = 5.3% ==> 0.053

,

• Number of times compounded = quarterly = 4 times

Let's find the amount that must be deposited into the account quarterly.

Apply the formula:

FV=P(\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}})

Where:

FV is the future value = $28,000

r = 0.053

n = 4

t = 6 years

Thus, we have:

28000=P(\frac{(1+\frac{0.053}{4})^{4\times6}-1)}{\frac{0.053}{4}}

Let's solve for P.

We have:

\begin{gathered} 28000=P(\frac{(1+0.01325)^{24}-1}{0.01325}) \\  \\ 28000=P(\frac{(1.01325)^{24}-1)^{}}{0.01325}) \\  \\ 28000=P(\frac{1.371509114-1}{0.01325}) \\  \\ 28000=P(\frac{0.371509114}{0.01325}) \end{gathered}

Solving further:

28000=P(28.0384237)

Divide both sides by 28.0384237:

\begin{gathered} \frac{28000}{28.0384237}=\frac{P(28.0384237)}{28.0384237} \\  \\ 998.6=P \\  \\ P=998.6 \end{gathered}

Therefore, the amount that must be deposited quarterly into the account is $998.60

ANSWER:

$998.60

8 0
1 year ago
Intruduction to a scientific notation with negative exponenents.
alukav5142 [94]
10 to the negative sixth equals 1/60, and then times 4 equals 4/60 or 1/15
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You paint 1/3 of a wall in 1/4 hour. At that rate, how long will it take you to paint one wall?
jeka57 [31]
It will take you 3/4 of an hour, or 45 minutes to paint 1 wall.
8 0
3 years ago
Read 2 more answers
Andre and Jillian were shopping at the same grocery store for bottles of sports drinks for their kickball teams. Andre bought 3
Leno4ka [110]

Answer:

x = 4

Step-by-step explanation:

The equation comes out to be:

3x + 11 = 5x + 3

Move the <u>variables</u> to the left-hand side and change its sign

And move the <u>constant</u> to the right-hand side and change its sign:

3x - 5x = 3 - 11

Combine like terms to get:

-2x = -8

Isolate x by dividing -2 on both sides:

-2x/-2 = -8/-2

x = 4

6 0
2 years ago
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