Rick surveyed 50 students at his school to see how many have after-school jobs and how many are getting the new video game conso

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.

Answer: After the withdrawal, Rajan's bank balance will be

6150 RS - 2050 RS = 4100 RS

Step-by-step explanation:

Initially, Rajan had 6000 RS in his bank account about a week ago. This indicates that the initial balance he possessed is 6000 RS.

One week later, he credited 150p RS to his account.

Thus, the current total in his account is

= 6000 RS + 150p RS = 6150 RS.

The following day, he withdrew one-third of his total balance. Therefore, the amount withdrawn is

1/3 × 6150 = 6150/3 = 2050 RS

After the withdrawal, his remaining balance in the bank will be the new total minus the amount withdrawn.

His remaining balance in the bank account post-withdrawal will be

6150 RS - 2050 RS = 4100 RS

<span>Denote x as the interval, then: 186 = 50 + 3 + (3+x) + (3+2x) + (3+3x) + (3+4x) + (3+5x) + (3+6x) + (3+7x) 186 = 74 + 28x x = 4 Age of the eldest son = 3+7x = 3+28 = 31.</span>

a) The specified probability distribution is b) 0.5, representing a 50% chance that X assumes a value between 21 and 25. c) 0.25 denotes a 25% likelihood that X takes on a value of at least 26. A uniform probability distribution encompasses two limits, a and b. The probability of obtaining a value lower than x is calculated accordingly. Also, the likelihood of finding a value between c and d is defined in correlation with the observed uniform distribution ranging from 20 to 28.

Response:

x² + -6x = -13

Detailed breakdown:

8x² - 48x = -104

Rearranging gives us x² - 6x = -13