A single die is rolled 5 times. Find the probability of getting at least one num

Question

A single die is rolled 5 times. Find the probability of getting at least one number which is greater than 4. Given data values: 11, 3, 5, 12, 17, 13, 10, 6, 8, 21, 14, 20, 9, 15, 7. (a) Find the tie for 10. (b) What value corresponds to the 70^th percentile? A survey found that the American family generates an average of 25 pounds of glass garbage each year. Assume the standard deviation of the distribution is 7 pounds. Find the probability that the mean of a sample of 49 families will be between 19 and 26 pounds.

Explanation / Answer

#3

P(at least 1 number is greater than 4) = 1 – P(None of the 5 numbers is greater than 4)

= 1 – P(all of the 5 numbers are less than or equal to 4)

= 1 – (4/6)5

= 0.8683

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#4

First arrange data in ascending order.

a)

10 is 7th highest score in the distribution, so R=7. We also know that there are N=15 scores.

The percentile rank formula is: P = 100R/(N+1) = 100*7/(15+1) = 43.75.

b)

For 70th percentile:

0.7*15=10.5 or 11

Form sorted data, 11th number is 14. Therefore, 70th percentile for data is 14.

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#5

x= = 25

x= /n = 7/49 = 1

P(19 < x < 26) = P((19-25)/1 < z < (26-25)/1) = P(-6 < z < 1) = 0.8413-0 = 0.8413

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