A Vending Machine Automatically Pours Soft Drinks Into Cups. The Amount Of Soft Drink Dispensed Into A Cup Is
January 18th, 2010 Posted in Información General
normally distributed with a mean of 7.6 oz and standard deviation of 0.4 oz
(a) Estimate the probability that the machine will overflow an 8-oz cup.
(b) Estimate the probability that the machine will NOT overflow an 8-oz cup.
(c) The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?
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blackout roller blinds Says:
January 18th, 2010 at 11:38 pm
Given:
normal distribution sample
u = mean = 7.6 oz
s = standard deviation = 0.4 oz
Solution:
(a) P = ? for x > 8 oz
Solving for z yields
z = (x - u) / s = (8 - 7.6) / 0.4 = 1
From the z-tables P(1) = 0.8413 (answer to b) for x< = 8 oz, therefore x > 8 oz is
P(x>8) = 1 - 0.8413 = 0.1587 (15.87%)
(b) P = ? for x < = 8 oz
As derived from the z-tables (as shown above)
P = 0.8413 (or 84.13%)
(c) For N = 850 cups determine n with x > 8 oz.
n = N * P(x>8) = 850 (0.1587) = 134.9
= 135 cups
Here’s a helpful site for TI-83/85 users http://mathbits.com/MathBits/TISection/S…
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WP Robot Wordpress Autoposter Says:
January 18th, 2010 at 11:38 pm
For mu=7.6, sd=0.4
= P(z>1) = 0.1587
= 1 - 0.1587 =0.8413
a)
P( x >
b) P(x<8) = 1 - P( x >
c) Number overflowing = 850 x 0.1587 =134.86 =135 approx