Suppose x is a normally distributed random variable with muÎ¼equals=1212

and

sigmaÏƒequals=22.

Find each of the following probabilities.

**a.** P(xgreater than or equalsâ‰¥13.513.5)

**b.**

P(xless than or equalsâ‰¤8.58.5)

**c.**

P(13.3813.38less than or equalsâ‰¤xless than or equalsâ‰¤17.5417.54)

**d.**

P(7.427.42less than or equalsâ‰¤xless than or equalsâ‰¤14.914.9)

One method of purification of molten salt involves oxidation. An important aspect of the purification process is the rising velocity of oxygen bubbles in the molten salt. An experiment was conducted in which oxygen was inserted (at a designated sparging rate) into molten salt and photographic images of the bubbles taken. A random sample of 2525

images yielded the data on bubble velocity (measured in meters per second) shown in the accompanying table. Complete parts a and b below.

Click the icon to view the table of bubble velocity data.

**a.** Use technology to find a 9595%

confidence interval for the mean bubble rising velocity of the population. Interpret the result.

The confidence interval is left parenthesis nothing comma nothing right parenthesis

,

.

(Type integers or decimals rounded to three decimal places as needed.)

Interpret the result. Select the correct choice below and fill in any answer boxes to complete your choice.

(Round to three decimal places as needed. Use ascending order.)

With nothing%

confidence, the true mean bubble rising velocity is between

nothing

and

nothing.

With nothing%

confidence, the true variance of the bubble rising velocity is between

nothing

and

nothing.

With nothing%

confidence, the true mean bubble rising velocity is exactly

nothing.

**b.** The researchers discovered that the mean bubble rising velocity is muÎ¼equals=0.3410.341

when the sparging rate of oxygen is

3.363.36timesÃ—10 Superscript negative 610âˆ’6.

Do you believe that the data in the table were generated at this sparging rate? Explain. Choose the correct answer below.

Yes. The discovered mean velocity is close enough to the confidence interval calculated in part a that it is reasonable for these data to have been generated using this sparging rate.

No. The discovered mean velocity is equal to one of the bounds of the confidence interval. Since the bounds are not included in the interval, it is not reasonable that these data could have been generated using this sparging rate.

Yes. The discovered mean velocity lies near the center of the confidence interval calculated in part a. Thus, it is very likely that these data were generated using this sparging rate.

No. The discovered mean velocity lies well outside the confidence interval calculated in part a. Thus, it is very unlikely that these data were generated using this sparging rate.

Click to select your answer(s).