Players in sports are said to have "hot streaks" and "cold streaks." For example, a batter in baseball might be considered to be in a slump, or cold streak, if that player has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 41% of the time he comes to the plate. Complete parts (a) through (c) below (a) Find the probability that the hitter makes 10 outs in 10 consecutive at-bats, assuming at-bats are independent events. Hint The hitter makes an out 59% of the time P(hitter makes 10 consecutive outs) = 0. 00511 (Round to five decimal places as needed.) (b) Are cold streaks unusual? The probability of a cold streak is less than 0.05, so cold streaks unusual. are (c) Interpret the probability from part (a). In repeated sets of 10 consecutive at-bats, the hitter is expected to make an out in all 10 at-bats about times out of 1000 (Type a whole number)

Q: The table below shows the predicted testing outcome for a disease that affects 2% of a population,…

A: Given,   Positive Test Negative Test Total Has Disease 18 2 20 Does Not Have Disease 98 882…

Q: The life of automobile voltage regulators has an exponential distribution with a mean life of six…

A: Given Mean=6 X=5

Q: The probability of a resident of a certain city being the victim of a serious crime at some point in…

A: It is an important part of statistics. It is widely used.

Q: A certain insecticide kills 50% of all insects in laboratory experiments. A sample of 7 insects is…

A: The objective of this question is to find the probability that exactly 4 out of 7 insects will…

Q: The chance of rain is 20%, the chance of it being sunny is 60%, and the chance of it being sunny and…

A: Let us denote  R=rain S=sunny Given that P(R)=20%=0.20, P(S)=60%=0.60, P(R and S)=10%=0.10

Q: The price of a stock is $45. The expected annual return on the stock is 15% and the volatility is…

A: From given data we have: Expected annual return = 15% Volatility = 50% The probability that the…

Q: Find the probability of the indicated event if ​P(E)=0.25 and P(F)=0.45.

A: From the given information, ​P(E)=0.25 and P(F)=0.45 P(E and​F)=0.10.

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!