1) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 70° F to 91°F.What is the probability that a randomly selected August day has a high temperature that exceeded 75°F?
2) A random variable X is normally distributed with µ=60.Convert the value of X to Z-score,if the standard deviation is as given. X=63; s =3
3) Find the area under the standard normal curve between z=0 and z=3.
4) Find the area under the standard normal curve to the right of z=1.
5) For a standard normal curve, find the z-score that seperates the bottom 90% from the top 10%.
6) For a standard normal curve, find the z-score that seperates the bottom 30% from the top 70%.
7) IQ test scores are normally distributed with the mean of 102 and the standard deviation of 13. An individual's IQ score is found to be 107.Find the z-score corresponding to this value.
8) IQ test scores are normally distributed with the mean value of 101 and the standard deviation of 13. An individuals IQ score is found to be 103. Find the z-score corresponding to this value. Suppose the price of new homes are normally distributed with the mean value of $150,000. Find the percentage of buyers who paid:
9) between $148,000 and $151,200 if the standard deviation is $1200.
10) between $150,000 and $151,800 if the standard deviation is $900.
11) A physical fitness association is including the mile run in its secondary-school fitnesstest.The time for this event for boys in secondary school is known to posses a normal distribution with a mean of 440 seconds and a standard deviation of 50 seconds.The fitness association wants to recognize the fastest %10 percent of boys with certificates of recognition.What time would the boys need to beat in order to earn a certificae of recognition from the fitness association?
12) A student answers all 48 questions on a multiple-chice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets excatly 15 correct answers. Use the normal distribution to approximate the binomial distribution.
13) If the probability of a newborn child bieng female is 0.5, find the probability that in 100 births, 55 or more will be female.Use the normal distribution to approximate the binomial distribution.