The semicircle shown at left has center X XX and diameter W Z ‾ ​WZ ​ ​​ start overline, W, Z, end overline. The radius X Y ‾ ​X

Answer:

F(n)= 0.50+0.15

Step-by-step explanation:

The starting point is 0.50. Additionally, when adding a fine of 0.15, you would consider 0.15 as well.

Answer:

The likelihood that a failure will not take place within the next 30 months is 0.0454.

Step-by-step explanation:

We employ a Poisson distribution where:

t = time units

x = occurrences during t units

λ = average occurrences per unit of time

P(x;λt) = e raised to the power of (-λt) multiplied by λtˣ divided by x!

Here, λt equals 25.

x equals 30.

P(x= 30) = 25³⁰e⁻²⁵/ 30!

P (x= 30) = 8.67 E41 * 1.3887 E-11/30!    (where E signifies exponent)

P (x=30) = 1.204 E31/30!

Utilizing a statistical calculator will yield:

P (x=30) = 0.0454

The probability that the next failure will not occur prior to 30 months is 0.0454.

Answer:

The range of cheerleaders' heights lies within the interval [58, 74)

It includes all real numbers from 58 inches and above, but below 74 inches.

Step-by-step explanation:

we have

Separate the combined inequality into two distinct inequalities

-----> inequality A

-----> inequality B

Solve inequality A

Subtract 28 from both sides

Split by 4 on both sides

Reformulate

Address inequality B

Subtract 28 from both sides

Split by 4 on both sides

consequently

The height range of the cheerleaders is the interval [58, 74)

It consists of every real number starting from 58 inches and less than 74 inches

Answer:

Hence, in this case, the 98% confidence interval would be (163.626;180.374)    

Step-by-step breakdown:

Previous concepts

A confidence interval represents a range that is likely to encompass a population value within a specific confidence level, typically expressed as a percentage whereby a population mean falls between an upper and lower limit.

The margin of errorindicates the span of values surrounding the sample statistic in a confidence interval.

A normal distributionillustrates a probability distribution that is symmetrical around the mean, signifying that values near the mean occur more frequently than those farther away from it.

denote the sample mean

population mean (the variable of interest)

s=16 signifies the sample standard deviation

n=23 represents the sample size  

The solution to the query

The equation for the confidence interval of the mean is given by the following formula:

  (1)

To determine the critical value , we first need to calculate the degrees of freedom, which is expressed as:

Since the confidence level is 0.98 or 98%, we find the value of and using tools like Excel or a calculator, where the Excel command would be: "=-T.INV(0.01,22)". This yields

Having all components ready, we can substitute into formula (1):

Thus, for this case, the 98% confidence interval will be (163.626;180.374)