Suppose only 75% of all drivers in a certain state regularly wear a seat belt. a random sample of 500 drivers is selected. what is the probability that a. between 360 and 400 (inclusive) of the drivers in the sample regularly wear a seat belt? b. fewer than 400 of those in the sample regularly wear a seat belt? devore, jay l.. probability and statistics for engineering and the sciences (p. 169). cengage learning. kindle edition.

a.   0.93449

b. 0.99506

Step-by-step explanation:

Given : The proportion of all drivers in a certain state regularly wear a seat belt : p=0.75

Sample size : n=500

Let x be the random variable that represents the number of drivers in a certain state regularly wear a seat belt.

Then ,

a.  The probability that between 360 and 400 (inclusive) of the drivers in the sample regularly wear a seat belt :

∴ The probability that between 360 and 400 (inclusive) of the drivers in the sample regularly wear a seat belt= 0.93449

b. The probability that fewer than 400 of those in the sample regularly wear a seat belt :-

∴ The probability that fewer than 400 of those in the sample regularly wear a seat belt = 0.99506

a

step-by-step explanation:

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