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stepan [7]
3 years ago
12

Construct a 95% confidence interval for the population mean, µ. Assume the population has a normal distribution. A sample of 25

randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2.
Mathematics
1 answer:
Alex787 [66]3 years ago
5 0

Answer:

Step-by-step explanation:

We want to determine a 95% confidence interval for the mean mean test score of students.

Number of sample, n = 25

Mean, u = 81.5

Standard deviation, s = 10.2

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z score ×standard deviation/√n

It becomes

81.5 ± 1.96 × 10.2/√25

= 81.5 ± 1.96/× 2.04

= 81.5 ± 3.9984

The lower end of the confidence interval is 81.5 - 3.9984 =77.5

The upper end of the confidence interval is 81.5 + 3.9984 = 85.5

Therefore, with 95% confidence interval, the mean test score of students is between 77.5 and 85.5

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El angulo de elevacion del sol es de 29°12'35''. Calcular la longitud de la sombra proyectada por un hombre de 1,75m de estatura
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Respuesta:

3,59 metros

Explicación paso a paso:

Conversión del ángulo de elevación a grados;

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= 29 ° + 12 '/ 60 + 35 "/ 3600

= 29,20972 °

Resolviendo el triángulo de solución adjunto:

La longitud de la sombra se puede obtener utilizando la relación trigonométrica;

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A closed cylindrical tank has a height of 200 cm and a diameter of 126 cm
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4 0
4 years ago
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There are seven cats in my neighborhood, with an average of $41$ whiskers each. If one of the cats has $17$ whiskers, how many w
harkovskaia [24]

Answer:

Each of the other cats have 45 whiskers on average.

Step-by-step explanation:

Let x represent the average number of whisker of each cat.

We have been given that there are 7 cats in my neighborhood, with an average of 41 whiskers each.

The total number of whiskers of six cats would be 6x.

Since one of the cats has 17 whiskers, so the total number of whiskers of 7 cats would be 6x+17

We will use average formula to solve our given problem.

\text{Average}=\frac{\text{Sum of data points}}{\text{Number of data points}}

Upon substituting our given values, we will get:

41=\frac{6x+17}{7}

Let us solve for x.

41*7=\frac{6x+17}{7}*7

287=6x+17

287-17=6x+17-17

270=6x

Switch sides:

6x=270

\frac{6x}{6}=\frac{270}{6}

x=45

Therefore, the each of the other cats have 45 whiskers on average.

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Are you able to expand everything first? from there you would be able to combine line terms. basically if you have 3x+2x it would combine to 5x because they have x in them.
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