6. 0/1.66 points | Previous Answers BBUnderSta1116.6.009. My Notes Ask Your Teac

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6. 0/1.66 points | Previous Answers BBUnderSta1116.6.009. My Notes Ask Your Teacher In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Round your answers It is estimated that 3.2% of the general population will live past their 90th birthday. In a graduating class of 760 high school seniors, find the following probabilities to four decimal places.) (a) 15 or more will live beyond their 90th birthday 0.9726 (b) 30 or more will live beyond their 90th birthday (c) between 25 and 35 will live beyond their 90th birthday (d) more than 40 will live beyond their 90th birthday Need Help? Read

Explanation / Answer

p = 0.032 n = 760

Mean = n * p = 760 * 0.032 = 24.32.

Standard deviation = (np(1-p)) = (24.32*0.968) = 23.54176 = 4.8520.

Since both np and n(1-p) are greater than 10, it is possible to approximate normally.

(a) x >= 15

=> x = 14.5

z = (x - ) /

= (14.5 - 24.32) / 4.8520

= -2.0239.

Probability from tables (right tailed) = 0.9785.

(b) x >= 30

=> x = 29.5

z = (x - ) /

= (29.5 - 24.32) / 4.8520

= 1.0676.

Probability from tables (right tailed) = 0.1429.

(c) 25 <= x <= 35

=> 24.5 <= x <= 35.5

=> (24.5 - 24.32) / 4.8520 <= z <= (35.5 - 24.32) / 4.8520

=> 0.0371 <= z <= 2.3042

P(0.0371 <= z <= 2.3042) = 0.9894 - 0.5148 = 0.4746.

(d) x > 40

=> x = 40.5

z = (x - ) /

= (40.5 - 24.32) / 4.8520

= 3.3347.

Probability from tables (right tailed) = 0.0004.

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