MATHEMATICS COLLEGE

Every morning Jack flips a fair coin ten times. He does this for anentire year. LetXbe the number of days when all the flips come out the same way(all heads or all tails).(a) Give the exact expression for the probabilityP(X >1).(b) Is it appropriate to approximateXby a Poisson distribution

Answers

Answer 1

Answer:

Answer:

See the attached picture for detailed answer.

Step-by-step explanation:

See the attached picture for detailed answer.

Answer 2

Answer:

Final answer:

The probability question from part (a) requires calculating the chance of getting all heads or all tails on multiple days in a year, which involves complex probability distributions. For part (b), using a Poisson distribution could be appropriate due to the rarity of the event and the high number of trials involved.

Explanation:

The question pertains to the field of probability theory and involves calculating the probability of specific outcomes when flipping a fair coin. For part (a), Jack flips a coin ten times each morning for a year, counting the days (X) when all flips are identical (all heads or all tails). The exact expression for P(X > 1), the probability of more than one such day, requires several steps. First, we find the probability of a single day having all heads or all tails, then use that to calculate the probability for multiple days within the year. For part (b), whether it is appropriate to approximate X by a Poisson distribution depends on the rarity of the event in question and the number of trials. A Poisson distribution is typically used for rare events over many trials, which may apply here.

For part (a), the probability on any given day is the sum of the probabilities of all heads or all tails: 2*(0.5^10). Over a year (365 days), we need to calculate the probability distribution for this outcome occurring on multiple days. To find P(X > 1), we would need to use the binomial distribution and subtract the probability of the event not occurring at all (P(X=0)) and occurring exactly once (P(X=1)) from 1. However, this calculation can become quite complex due to the large number of trials.

For part (b), given the low probability of the event (all heads or all tails) and the high number of trials (365), a Poisson distribution may be an appropriate approximation. The mean (λ) for the Poisson distribution would be the expected number of times the event occurs in a year. Since the probability of all heads or all tails is low, it can be considered a rare event, and the Poisson distribution is often used for modeling such scenarios.

Learn more about Probability here:

brainly.com/question/32117953

#SPJ3

Answer with explanation:

Let $\mu$ be the population mean.

Null hypothesis : $H_0:\mu\geq26$

Alternative hypothesis : $H_1:\mu<26$

Since the alternative hypothesis is left tailed, so the test is a left-tailed test.

Sample size : n=5 <30 , so we use t-test.

Test statistic: $t=\frac{\overline{x}-\mu}{(\sigma)/(√(n))}$

$t=(25.2-26)/((1)/(√(5)))\approx-1.79$

Critical t-value for t= $t_(n-1, \alpha)=t_(4,0.06)=1.9712$

Since, the absolute value of t (1.79) is less than the critical t-value , so we fail to reject the null hypothesis.

Hence, we have sufficient evidence to support the company's claim.

John ordered five large size pizzas for a party. Five kids each ate 1/10 slice, and twelve adults each at 3/10 slices.a) Find the total number of slices consumed.
41/10
b) Find the leftover pizza if any.