A biologist estimates that 80% of the deer in a region carry a certain type of tick. for a sample of 300 deer selected at random

(1) The sample mean stands at 1480 hours while the population standard deviation is 80 hours.(2) The null hypothesis posits that the average lifespan of fluorescent bulbs is 1500 hours.(3) The critical value is 1.645.(4) The test statistic is D, -1.58.(5) The conclusion is B, we reject H0.(6) Thus, the conclusion indicates A, there isn't sufficient evidence to substantiate the claim that the average lifespan of its fluorescent bulbs is 1500 hours.

Answer:

(A) 0.15625

(B) 0.1875

(C) Cannot be determined

Step-by-step explanation:

The time it takes for a student to finish a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let's denote X as the duration needed for the student to complete the statistics quiz

Thus, X ~ U(32, 64)

The probability density function (PDF) for a uniform distribution is expressed as;

f(X) = ,  a < X < b      where a = 32 and b = 64

The cumulative distribution function (CDF) is given by P(X <= x) =

(A) The probability of a student taking longer than 59 minutes to complete the quiz = P(X > 59)

   P(X > 59) = 1 - P(X <= 59) = 1 - = 1 - = = 0.15625

(B) The probability that a student completes the quiz between 37 and 43 minutes = P(37 <= X <= 43)  = P(X <= 43) - P(X < 37)

    P(X <= 43) = = = 0.34375

    P(X < 37) = = = 0.15625

    P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

(C) The probability that a student takes exactly 44.74 minutes to complete the quiz

     = P(X = 44.74)

This probability cannot be calculated as it is a continuous distribution, which doesn't provide probabilities for specific points.

To determine the time interval δt, we must subtract the starting time from the ending time. In this scenario, the first value in the coordinates signifies time:

δt=50 - 0
δt= 50s

The time interval is 50s.

Each tweet could cost anywhere from 1 to 140 pennies, which can be expressed as an inequality [1 ≤ x ≤ 140]. Since it's impossible to tweet 0 characters or exceed 140. If required in pounds, simply divide by 100. A) 1 ≤ x ≤ 140 B) The cost per character is a penny, and tweeting fewer than 1 character or more than 140 is not permitted.