An athlete jumped 5.5 feet which was 1.1 times higher than the previous jumper how high did the previous athlete jump

Response:

Null hypothesis = H₀ = σ₁² ≤ σ₂²

Alternative hypothesis = Ha = σ₁² > σ₂²

Calculated statistic = 1.9

p-value = 0.206

Given that the p-value exceeds α, we do not reject the null hypothesis.

Thus, we conclude that night shift workers do not exhibit higher variability in their output levels compared to day workers.

Step-by-step elaboration:

Let σ₁² represent the variance for night shift workers

Let σ₂² represent the variance for day shift workers

State the null and alternative hypotheses:

The null hypothesis suggests that the variance of night shift workers does not exceed that of day shift workers.

Null hypothesis = H₀ = σ₁² ≤ σ₂²

The alternative hypothesis posits that the variance for night shift workers surpasses that of day shift workers.

Alternative hypothesis = Ha = σ₁² > σ₂²

Calculated statistic:

The test statistic, or F-value, is derived using

Test statistic = Larger sample variance/Smaller sample variance

The larger sample variance is σ₁² = 38

The smaller sample variance is σ₂² = 20

Test statistic = σ₁²/σ₂²

Test statistic = 38/20

Calculated statistic = 1.9

p-value:

The corresponding degrees of freedom for night shift workers is[1]

df₁ = n - 1

df₁ = 9 - 1

df₁ = 8

The corresponding degrees of freedom for day shift workers is[1]

df₂ = n - 1

df₂ = 8 - 1

df₂ = 7

We can obtain the p-value using the F-table or Excel.

To determine the p-value in Excel, we use

p-value = FDIST(F-value, df₁, df₂)

p-value = FDIST(1.9, 8, 7)

p-value = 0.206

Conclusion:

p-value > α    

0.206 > 0.05   ( α = 0.05)As the

p-value is larger than α, we do not reject the null hypothesis with a confidence level of 95%

[[TAG_101]]This leads us to conclude that night shift workers do not demonstrate more variability in their output levels in comparison to day workers.[[TAG_102]]

18

He can combine one hat with a scarf, resulting in 18 different combinations for Sam when multiplying 6 by 3.

Respuesta:

P = 2/7 = 0.2857 o 28.57%

Explicación paso a paso:

En primer lugar, sabemos que hay 15 bolas y necesitamos identificar cuáles son pares y superiores a 10.

Por lo tanto, debemos calcular inicialmente la probabilidad de que el número obtenido sea par.

Los números pares son 2, 4, 6, 8, 10, 12, 14

Contamos 7 números de 15 ---> P(B) = 7/15

De esos números, solo dos son mayores a 10, que son 12 y 14, así que: P(A|B) = 2/15

Para encontrar la probabilidad de obtener un número par mayor que 10:

P(A/B) = P(A|B) / P(B)

P(A/B) = 2/15 / 7/15 = 2/7 = 0.2857

Para calcular el porcentaje: 0.2857 * 100 = 28.57%.

This scenario relates to binomial probability, where the results can either be a success or a failure. A success indicates that a selected adult possesses a bachelor's degree. Consequently, the success probability, denoted as p, is 20/100 = 0.2. The number of adults in the sample, represented as n, equals 100, and x, the count of successes, is 60. The probability of having more than 60 adults with a bachelor's degree, represented as P(x >60), can be noted internally as P(x < 60) = binomcdf (100, 0.20, 60). The function binompdf would indicate P(x = 60).

In certain cases, a function necessitates multiple formulas to achieve the desired outcome. An example is the absolute value function \displaystyle f\left(x\right)=|x|f(x)=∣x∣. This function applies to all real numbers and yields results that are non-negative, defining absolute value as the magnitude or modulus of a real number regardless of its sign. It indicates the distance from zero on the number line, requiring all outputs to be zero or greater.

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\displaystyle f\left(x\right)=x\text{ if }x\ge 0f(x)=x if x≥0

<pwhen inputting="" a="" negative="" value="" the="" output="" is="" inverse:="">

\displaystyle f\left(x\right)=-x\text{ if }x<0f(x)=−x if x<0

Due to the need for two distinct operations, the absolute value function qualifies as a piecewise function: a function defined by several formulas for different sections of its domain.

Piecewise functions help describe scenarios where rules or relationships alter as the input crosses specific "boundaries." Business contexts often demonstrate this, such as when the cost per unit of an item decreases past a certain order quantity. The concept of tax brackets also illustrates piecewise functions. For instance, in a basic tax system where earnings up to $10,000 face a 10% tax, additional income incurs a 20% tax rate. Thus, the total tax on an income S would be 0.1S when \displaystyle {S}\leS≤ $10,000 and 1000 + 0.2 (S – $10,000) when S > $10,000.

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