Prove that if a sequence of random variables X_1,X_2,... converges in probability to a random variable X, the sequence also converges in distribution

The distance advanced in a day by a tunnel boring machine, in meters, is uniformly distributed on the interval (31.00, 50). Suppose the distances advanced on different days are independent. What is the probability the machine advances more than 45 meters on exactly four out of 10 days? (Round the final answer to four decimal places.)   Probability =

According to the Central Limit Theorem, the distribution of sample means is NOT normal if _________________.   A) The population from which the samples are selected is not normally distributed and the sample size is small (n < 30).   B) The population from which the samples are selected is not normally distributed and the sample size is large (n >= 30).   C) The population from which the samples are selected is normally distributed and the sample size is small (n < 30).   D) The population from which the samples are selected is normally distributed and the sample size is large (n >= 30).

A man and a woman agree to meet at a cafe about noon. If the man arrives at a time uniformly distributed between 11:35 and 12:10 and if the woman independently arrives at a time uniformly distributed between 11:50 and 12:30, what is the probability that the first to arrive waits no longer than 55 minutes?