dave is helping his grandmother make trail mix his grandmother asks him to add 1/5 cup of fruit for every 1/3 cup of nuts. To sa

Answer: 0.5507

Step-by-step explanation:

Given: The time between sightings of speeders by a radar system is represented by the continuous random variable X, which follows a cumulative distribution function

If we convert 12 minutes into hours, it equals hours or 0.2 hours.

To find the probability of waiting less than 12 minutes:

Thus, the probability we are looking for is: 0.5507

Response:

a) S ~ N (0, 48)

b) P(S > 10) = 0.0745

Detailed explanation:

Given Information:-

- Total number of questions, n = 100

- Each question has 5 options

- The probability of correctly guessing each answer is independent.

- Points for a correct answer = +4

- Points for an incorrect answer = -1

Inquiries:-

a) Determine????(S).

b) Determine P(S>10). Represent your response as a mathematical formula, then utilize the code cell below to calculate its numerical value, providing both the calculation and its result.

Solution:-

- The probability (p) for answering a question correctly is:

p (correct answer) = 1/5 = 0.2

- The expected number of correct and incorrect answers can be calculated as follows:

(Expected correct answers) = n*p = 100*0.2 = 20

(Expected incorrect answers) = n*(1-p) = 100*0.8 = 80

- The anticipated score for correct answers will be:

Sc(u) = (Points for a correct answer)*(Expected correct answers)

Sc(u) = (+4)*(20)

Sc(u) = 80 points

The anticipated score for incorrect answers will be:

Si(u) = (Points for an incorrect answer)*(Expected incorrect answers)

Si(u) = (-1)*(80)

Si(u) = -80 points.

- The average score a student might achieve would be S(u):

S(u) = Sc(u) + Si(u)

S(u) = 80 - 80 = 0

- The variance for both correct and incorrect answers can be calculated as:

Var(correct answers) = n*p*q = 100*0.2*0.8 = 16

Var(incorrect answers) = n*p*q = 100*0.2*0.8 = 16

- The variance of points for correct answers can be expressed as:

Sc(Var) = Var(correct answer) * (Points for a correct answer)

Sc(Var) = 16*(+4) = +64 points

- The variance of points for incorrect answers can be expressed as:

Si(Var) = Var(incorrect answer) * (Points for an incorrect answer)

Si(Var) = 16*(-1) = -16 points

- Since the probabilities of correct guesses are independent, according to the independence principle:

S(Var) = Sc(Var) + Si(Var)

= 64 - 16

= +48 points

- The standard deviation for the score distribution (s.d) is:

S(s.d) = √S(Var) = √48 = 6.9282

- Therefore, the anticipated score (S) from guessing on the MCQ test would yield a mean of u = 0 points and s.d = + 48 points.

- The random variable (S) can be approximated using normal distribution as follows:

S ~ N (0, 48)

- To find the required probability P(S>10).

Calculate the Z-value for S = 10 points:

Z-value =  ( S - u ) / s.d

=  ( 10 - 0 ) / 6.9282

= 1.4434

Consult the standardized Z-table for normal distribution:

P(Z > 1.4434) = 0.0745

The probability is:

P(S > 10) = P(Z > 1.4434) = 0.0745