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.
It is estimated that 3.5% of the general population will live past their 90th birthday. In a graduating class of 751 high school seniors, find the following probabilities. (Round your answers to four decimal places.)
(a) 15 or more will live beyond their 90th
birthday
(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
n = 751
p = 0.035
= n * p = 751 * 0.035 = 26.32
= sqrt(np(1 - p))=5.04
a) 0.9904
x | 14.5 |
Using(x-u)/sd | -2.33998 |
Using Standard Normal table | 0.0096 |
step 1-0.0096 | 0.9904 |
b) 0.2616
x | 29.5 |
Using(x-u)/sd | 0.638357 |
Using Standard Normal table | 0.7384 |
step 1-0.7384 | 0.2616 |
c) 0.6048
x | 24.5 | 35.5 |
Using(x-u)/sd | -0.3544 | 1.8297 |
Using Standard Normal table | 0.3615 | 0.9664 |
Difference | 0.6048 |
d) 0.0024
x | 40.5 |
Using(x-u)/sd | 2.822469 |
Using Standard Normal table | 0.9976 |
step 1-0.9976 | 0.0024 |
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