Which of the following statement(s) is/are TRUE for a given acceptance sampling plan?
- Type II error decreases with an increase in type I error.
- The probability of rejecting a good quality lot is producer's risk.
- Type II error decreases with a decrease in sample size.
- The probability of rejecting a good quality lot is consumer's risk.
The Correct Option is A, B
Solution and Explanation
Top Questions on Probability
- The probability that a student buys a colouring book is 0.7, and a box of colours is 0.2. The probability that she buys a colouring book, given that she buys a box of colours, is 0.3. Find:
(i) The probability that she buys both the colouring book and the box of colours.
(ii) The probability that she buys a box of colours given she buys the colouring book. - A fruit box contains 6 apples and 4 oranges. A person picks out a fruit three times with replacement. Find:
(i) The probability distribution of the number of oranges he draws.
(ii) The expectation of the number of oranges. Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.
- A coin is tossed and a card is selected at random from a well shuffled pack of 52 playing cards. The probability of getting head on the coin and a face card from the pack is:
Two persons are competing for a position on the Managing Committee of an organisation. The probabilities that the first and the second person will be appointed are 0.5 and 0.6, respectively. Also, if the first person gets appointed, then the probability of introducing a waste treatment plant is 0.7, and the corresponding probability is 0.4 if the second person gets appointed.
Based on the above information, answer the following
Questions Asked in GATE PI exam
- The left-hand side of a 20 cm thick wall is maintained at 25°C. The right-hand side of the wall is exposed to hot air at 50°C. There is no heat generation inside the wall and its thermal conductivity is 100 W/m·K. The convective heat transfer coefficient is 50 W/m²·K. Under steady state condition, the temperature (in °C) of the right-hand side surface of the wall is ........ (Rounded off to one decimal place).
- GATE PI - 2025
- Heat Transfer and Associated Losses
- Water flows through a smooth circular pipe of diameter 10 cm and length 10 m. The pressure drop across the length of the pipe is 0.2 Pa. Kinematic viscosity and density of water are \(1 \times 10^{-6} \, {m}^2/{s}\) and 1000 \({kg/m}^3\), respectively. Assuming laminar and fully developed flow throughout the pipe, the velocity of water (in mm/s) at the center of the pipe is ........ (Rounded off to one decimal place)
- GATE PI - 2025
- Fluid Mechanics
The table shows the data of running a machine for five years. The original machine cost is Rupees 70,000. In order to minimize the average total cost per year for running the machine, the machine should be replaced after ............. years. (Answer in integer)
- GATE PI - 2025
- Economic Activities
- The zero line of the Vernier scale lies between divisions 20 and 21 of the main scale. The 4th Vernier scale division exactly coincides with a main scale division. The 5 divisions of the Vernier scale are equal to 4 divisions of the main scale. If one main scale division is 1 mm, the measured value (in mm) is ........... (Rounded off to one decimal place)
- GATE PI - 2025
- Industrial and Production
A company purchases items in bulk for getting quantity discounts in the item’s price. The price break-up is given in the table. The annual demand for the item is 5000 units. The ordering cost is Rupees 400 per order. The annual inventory carrying cost is 30 percent of the purchase price per unit. The optimal order size (in units) is .......... (Answer in integer)
- GATE PI - 2025
- Industrial and Production