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Anestetic [448]
1 year ago
8

A regulation hockey puck must weigh between 5.5 and 6 ounces. The weights X of pucks made by a particular process are normally d

istributed with mean 5.75 ounces and standard deviation 0.11 ounce. Find the probability that a puck made by this process will meet the weight standard.
Mathematics
1 answer:
mr_godi [17]1 year ago
6 0

Answer:

P(5.5

And we can find this probability with this difference:

P(-2.27

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(5.75,0.11)  

Where \mu=5.75 and \sigma=0.11

We are interested on this probability

P(5.5

And we can use the z score formula given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(5.5

And we can find this probability with this difference:

P(-2.27

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Mr. Jackson invested a sum of money at 6% per year, and 3 times as much at 4%
bogdanovich [222]

Mr. Jackson invested $800 at 6% per year and $ 2400  at 4 % per year

<h3><u>Solution:</u></h3>

Mr. Jackson invested a sum of money at 6% per year, and 3 times as much at 4% per year.

Let the sum invested be ‘a’ and ‘3a’ at 6% per year and 4 % per year respectively

Also, his annual return totaled $144

We can form following equation on the basis of question:-

\begin{array}{l}{\text { Then, } \frac{a \times 6 \times 1}{100}+\frac{3 a \times 4 \times 1}{100}=\$ 144} \\\\ {\frac{6 a}{100}+\frac{12 a}{100}=144} \\\\ {\frac{6 a+12 a}{100}=144} \\\\ {\frac{18 a}{100}=144} \\\\ {18 a=14400} \\\\ {a=14400 \div 18}\end{array}

a = $800

The amount of money invested at 6% = a = 800

The amount of money invested at 4 % = 3a = 3(800) = 2400

So, the amount of money invested at 6% is $800 and the amount of money invested at 4% is $ 2400

4 0
1 year ago
What percent of four hours is 8 seconds
salantis [7]

60 minutes per hour

 4 x 60 = 240 minutes

60 seconds per minute

240 x 60 = 14400 seconds

8/14400 = 0.0005555

= 0.055 % round off to 0.06%

8 0
1 year ago
Jason’s savings account has a balance of $2179. After 5 years , what will the amount of interest be at 6% compounded quarterly?
satela [25.4K]

Answer:

$755.80

Step-by-step explanation:

Determine the compound amount first and then subtract the principal from it, to find the amount of interest.

The compound amount formula is A = P (1 + r/n)^(nt), where

P is the initial principal, r is the interest rate as a decimal fraction, n is the number of compounding periods per year, and t is the number of years.  Here, P = $2179; t = 5 yrs; r = 0.06; and n = 4 (quarterly compounding).

We get:

A = $2179(1 + 0.06/4)^(4*5), or $2179(1.015)^20, or $2179(1.347) = $2937.80.

The compound amount is $2934.80.  Subtracting the $2179 principal results in the interest earned:  $755.80.

5 0
2 years ago
A toy rocket is launched from a platform 33 feet above the ground at a speed of 83 feet per second. The height of the rocket in
kiruha [24]

Answer:

282ft

Step-by-step explanation:

83×3=249

249+33=282

4 0
1 year ago
There are four activities on the critical path, and they have standard deviations of 1, 2, 4, and 2. what is the probability tha
Anit [1.1K]

Standard deviations of the four activities of the critical path are 1,2,4,2.

Standard deviation of this critical path = Sum of square root of variance of this corresponding critical path

Standard deviation of critical path =\sqrt{1^2+2^2+4^2+2^2}

=\sqrt{1+4+16+4}

=\sqrt{25}

=5

Now we need to find the probability that the project will completed in 38 weeks given that its expected completion time is 40 weeks.

That is, we need to find P(X<38) :

z=\frac{38-40}{5}= \frac{-2}{5}=-0.4

P(X

Probability =0.5-0.16=0.34

Thus the probability that the project will be completed in 38 weeks is 0.34.

8 0
2 years ago
Read 2 more answers
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