Working with Distributions
1. This question has 3 part(s).
1.1. State the conditions that must be satisfied to be able to model a random variable with a binomial distribution
1.2. A fair spinner has 5 sectors labelled with the numbers 1 through 5. The spinner is spun and a fair coin is flipped, and the number the spinner lands on along with the result of the coin flip (heads or tails) are recorded. For each of the following cases, state with a reason whether or not a binomial distribution would be appropriate for modelling the specified random variable.
(i) If the coin lands on heads, then the random variable is the number of the sector that the spinner lands on times two. Otherwise is the number of the sector that the spinner lands on plus 10.
(ii) The random variable is the number of times the spinner is spun and the coin is flipped until an odd number on the spinner occurs together with tails on the coin.
(iii) The random variable is the number of times a prime number on the spinner occurs together with heads on the coin, when the spinner is spun and the coin is flipped 21 times.
(iv) Each time the spinner is spun and the coin is flipped, it is a ‘win’ if a square number on the spinner occurs together with heads on the coin, or it is a ‘loss’ if a non-square number on the spinner occurs together with tails on the coin. Any other outcome is a ‘draw’. The random variable is the number of losses when the spinner is spun and the coin is flipped twelve times.
1.3. For the random variable defined in (b)(i) above, give the name of the probability distribution that would be appropriate for modelling . Give the values(s) of any parameters.
Ai এর মাধ্যমে
১০ লক্ষ+ প্রশ্ন ডাটাবেজ
প্র্যাকটিস এর মাধ্যমে নিজেকে তৈরি করে ফেলো
উত্তর দিবে তোমার বই থেকে ও তোমার মত করে।
সারা দেশের শিক্ষার্থীদের মধ্যে নিজের অবস্থান যাচাই
Use an appropriate normal distribution to approximate the probability that in 1000 spins the number of times the ball lands neither on a red number nor on a black number is neither 80 or more nor less than 75.
On the roulette wheel at the Dunes Oddstacker casino, the probability of the ball landing on a red number is , and the probability of the ball landing on a black number is the same. In general, the majority of bettors will lose their bets if the ball lands neither on a red number nor on a black number.
The wheel is spun 50 times, and the ball lands on a number that is either red or black times.
Find \(P(44
In a separate experiment, the wheel is spun 1000 times and , the number of times the ball lands neither on a red number nor on a black number, is recorded.
Explain why a normal approximation would be appropriate in this case.
Due to a production error, 58% of Bobbie Sue dolls were manufactured with proportions that might be seen on a real human being. Plastic surgeons have been buying up these so-called ‘realie’ dolls, out of a concern that if too many of them are seen by the general public then numbers of people seeking plastic surgery will decrease.
A toy shop has received an order of 100 Bobbie Sue dolls. These may be assumed to represent a random sample.
Calculate the percentage error when an appropriate normal approximation is used to calculate probability that exactly 58 of thr 100 dolls are 'realie' dolls.
