Question

question 7 (1 point) saved
the july temperatures in toronto is uniformly distributed on the interval 25°-35°. what is p(x>30° )?
50%
60%
40%
10%
90%
question 8 (1 point)

1. which statement is true for a normal distribution?

a. outcomes near the middle of the distribution are more likely than outcomes far from the middle.
b. the left side of the distribution is not symmetric with the right side about the centre.
c. all outcomes are equally likely.
d. none of the above.
d
c
a
b

Explanation:

Question 7

Step1: Recall Uniform Distribution Probability Formula

For a uniform distribution on \([a, b]\), the probability density function is \(f(x)=\frac{1}{b - a}\) for \(a\leq x\leq b\), and the probability \(P(X > k)\) (where \(a\leq k\leq b\)) is calculated as \(P(X > k)=\frac{b - k}{b - a}\). Here, \(a = 25\), \(b = 35\), and \(k = 30\).

Step2: Substitute Values into the Formula

First, calculate \(b - a=35 - 25 = 10\). Then, calculate \(b - k = 35 - 30 = 5\). Now, find the probability: \(P(X > 30)=\frac{35 - 30}{35 - 25}=\frac{5}{10}=0.5 = 50\%\).

• Option A: In a normal distribution, the probability density function is highest at the mean (middle) and decreases as we move away from the mean, so outcomes near the middle are more likely than those far from the middle. This is correct.
• Option B: A normal distribution is symmetric about the mean, so the left and right sides about the center are symmetric. Thus, B is incorrect.
• Option C: In a normal distribution, not all outcomes are equally likely (unlike a uniform distribution). So C is incorrect.
• Option D: Since A is correct, D is incorrect.

Answer:

50%

Question 8