When Margo makes cheese ravioli, she uses both ricotta and mozzarella cheeses to make the filling. She often varies the proporti
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Answer:
a) P(x≥6)=0.633
b) P(4≤x≤8)=0.8989 (one standard deviation from the mean).
c) P(x≤7)=0.8328
Step-by-step explanation:
a) We can model this a binomial experiment. The probability of success p is the proportion of customers that prefer the oversize version (p=0.60).
The number of trials is n=10, as they select 10 randomly customers.
We have to calculate the probability that at least 6 out of 10 prefer the oversize version.
This can be calculated using the binomial expression:
b) We first have to calculate the standard deviation from the mean of the binomial distribution. This is expressed as:
The mean of this distribution is:
As this is a discrete distribution, we have to use integer values for the random variable. We will approximate both values for the bound of the interval.
The probability of having between 4 and 8 customers choosing the oversize version is:
c. The probability that all of the next ten customers who want this racket can get the version they want from current stock means that at most 7 customers pick the oversize version.
Then, we have to calculate P(x≤7). We will, for simplicity, calculate this probability substracting P(x>7) from 1.
Answer:
a) t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
b) x = 0,97 miles
c) t (min) = 1,24 hours
Step-by-step explanation: See Annex
Figure in annex shows a clear description of the situation
Let x be distance in miles between point P and where boat lands
A woman has to row a distance L
L = √ (4)² + (x)²
and the part to get to the town (which she has to walk)
d = ( 7 - x)
But we are required to give time as a function of x
distance = speed * time ⇒ t = distance / speed
Therefore
t(x) = [ √ (4)² + (x)²]/ 4 + ( 7 - x ) / 5
t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
Taking derivatives both sides of the equation
t¨(x) = ( 2x)*4 / 16√ (4)² + (x)²] - 5/25
t¨(x) = x/ 2√ (4)² + (x)²] - 1/5
t¨(x) = 0 x/ 2√ (4)² + (x)²] - 1/5 = 0
[ 5 x - 2√ (4)² + (x)²] = 0 ⇒ 5x = 2√ (4)² + (x)²] or
25 x² = 4 ( 4 + x²)
25 x² = 16 + 8x²
17x² = 16
x² = 16/17
x² = 0,941
x = 0,97 miles
And the distance walking to get to town
d = 7 - x d = 7 - 0,97
d = 6,03 miles
The least travel time is t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
t (min) = √ 16 + 0,94) /4 + 1,4 - 0,97/5
t (min) = 1,03 + 1,4 - 0,194
t (min) = 1,24 hours
