Question

In: Statistics and Probability

The Mean number of words per minute (WPM) read by sixth graders is 98 with a...

The Mean number of words per minute (WPM) read by sixth graders is 98 with a standard deviation of 20. If 57 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 4.41 WPM? ( round your answer to 4 Decimal places and show work)

Solutions

Expert Solution

Solution :

Given that,

mean = = 98

standard deviation = = 20

n = 57

= 98

= / n = 20 / 57 = 2.649

= 1 - P(98 - 4.41 < < 98 + 4.41)

= 1 - P(93.59 < < 102.41)

= 1 - P((93.59 - 98) / 2.649 <( - ) / < (102.41 - 98) / 2.649))

= 1 - P(-1.6648 < Z < 1.6648)

= 1 - {P(Z < 1.6648) - P(Z < -1.6648)}

= 1 - {0.952 - 0.048}

= 1 - 0.904

= 0.096

Probability = 0.0960   


Related Solutions

The mean number of words per minute (WPM) read by sixth graders is 99 with a...
The mean number of words per minute (WPM) read by sixth graders is 99 with a variance of 441. If 82 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by less than 3.69 WPM? Round your answer to four decimal places.
The mean number of words per minute (WPM) read by sixth graders is 83 with a...
The mean number of words per minute (WPM) read by sixth graders is 83 with a standard deviation of 12 WPM. If 89 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 1.4 WPM? Round your answer to four decimal places.
The mean number of words per minute (WPM) typed by a speed typist is 72 with...
The mean number of words per minute (WPM) typed by a speed typist is 72 with a variance of 100. What is the probability that the sample mean would differ from the population mean by more than 3.3 WPM if 43 speed typists are randomly selected? Round your answer to four decimal places.
The mean number of words per minute (WPM) typed by a speed typist is 149 with...
The mean number of words per minute (WPM) typed by a speed typist is 149 with a standard deviation of 14 WPM. What is the probability that the sample mean would differ from the population mean by less than 2.3 WPM if 88 speed typists are randomly selected? Round your answer to four decimal places.
The mean number of words per minute (WPM) typed by a speed typist is 123 with...
The mean number of words per minute (WPM) typed by a speed typist is 123 with a standard deviation of 14 WPM. What is the probability that the sample mean would differ from the population mean by more than 1 WPM if 52 speed typists are randomly selected? Round your answer to four decimal places.
Step 1 of 5: Suppose that the distribution of typing speed in words per minute (wpm)...
Step 1 of 5: Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 60 wpm and standard deviation 15 wpm. What is the probability that a randomly selected typist's speed is at most 60 wpm? Round your answer to one decimal place. What is the probability that a randomly selected typist's speed is between 45 and 90 wpm?  Round...
Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using...
Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 64 wpm and standard deviation 15 wpm. b. What is the probability that a randomly selected typists typing speeds is between 45 and 90 wpm? Round your answer to four decmial places. Would you be surprised to find a typist in tis pop. to excced 105 wpm? Suppose two...
Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using...
Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 68 wpm and standard deviation 17 wpm. What is the probability that a randomly selected typist's speed is at most 68 wpm? What is the probability that a randomly selected typist's speed is less than 68 wpm? What is the probability that a randomly selected typist's speed is between...
Mrs. Smith's reading class can read an average of 175 words per minute with a standard...
Mrs. Smith's reading class can read an average of 175 words per minute with a standard deviation of 20 words per minute. The bottom 6% of the class is to receive a special training session. What is the minimum number of words per minutes a student would need to read in order to get training?
an educational psychologist wishes to know the mean number of words a third grader can read...
an educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an estimate at the 99% level confidence. For a sample of 2006 third graders, the mean words per minute read was 27.2. assume a population standard deviation of 4.1. construct the confidence interval for the mean number of words a third grader can read per minute. Round your answer to one decimal place.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT