Caroline took a math test and got 19 out of 25 questions correct. What percent of the questions did she answer correctly? What p
1 answer:
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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.
To find the gradient of the tangent, we must first differentiate the function.
The gradient at x = 0 is given by evaluating f'(0).
The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.
The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so
Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).
So the point (0, -1) lies on the tangent. Substituting into the tangent equation: