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The idle time for taxi drivers in a day are normally distributed with an unknown population mean and standard deviation. If a ra

Svet_ta [12734]

Answer:

$172-2.51\frac{16}{\sqrt{23}}=163.626$

$172+2.51\frac{16}{\sqrt{23}}=180.374$

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.

$\bar X=172$ denote the sample mean

$\mu$ 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:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

To determine the critical value $t_{\alpha/2}$ , we first need to calculate the degrees of freedom, which is expressed as:

$df=n-1=23-1=22$

Since the confidence level is 0.98 or 98%, we find the value of $\alpha=0.02$ and $\alpha/2 =0.01$ using tools like Excel or a calculator, where the Excel command would be: "=-T.INV(0.01,22)". This yields $t_{\alpha/2}=2.51$

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

$172-2.51\frac{16}{\sqrt{23}}=163.626$

$172+2.51\frac{16}{\sqrt{23}}=180.374$

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

3 0

2 months ago

Sara’s little brother is getting ready to color the picture of a rainbow that Sara drew for him. To make the task easier for her

Zina [12379]

There are seven rainbow colors: red, orange, yellow, green, blue, indigo, and violet, so 7 possible choices. When two events occur in sequence, multiply their probabilities. With replacement: P(violet)=1/7 and P(orange)=1/7, so P(violet then orange)=1/7 * 1/7 = 1/49. Without replacement: after picking violet, P(orange)=1/6, so P(violet then orange)=1/7 * 1/6 = 1/42.

8 0

2 months ago

Read 2 more answers

Would $3.99$ million flies or $47,000,000$ ants have a greater mass? Approximately how much greater, in grams, would the greater

zzz [12365]

Answer:

Ants weigh approximately 118,615,000mg more.

Step-by-step explanation:

Based on a quick search, the average housefly weighs around 11.5mg, while an ant averages at 3.5mg. With these average weights, we can calculate the total weight of each species.

Flies: 3,990,000 * 11.5mg = 45,885,000mg

Ants: 47,000,000 * 3.5mg = 164,500,000mg

Consequently, it's clear that the 47 million ants possess a greater mass, specifically

164,500,000 - 45,885,000 = 118,615,000mg more

3 0

2 months ago