<1> The average cholesterol content of a certain brand of eggs is 210 (mg), and the standard deviation is 15 (mg). a) If a single egg is selected, find the probability that the cholesterol content will be more than 215 mg.(0.3707). b) If a sample of 25 eggs is selected, find the probability that the mean of the sample will be larger than 215 mg.(0.0475).
<2> A fair coin is tossed 500 times. Use the normal-curve approximation to find the probability of getting from 240 to 260 heads?(0.6528).
<3> A multiple-choice test has 60 questions, each with 5 possible answers of which only one is the correct answer. What is the probability that sheer guesswork yields from 10 to 14 correct answers?(0.582)
<4> From a box containing 3 white balls and 7 black balls, 30 balls are drawn with replacement. Find the probability of getting 9 and 10 white balls.(0.305)
<5> Given the normally distributed variable X with mean 40 and standard deviation 5, find
a) P( 35
<6> The IQs of 1000 applicants to a college are approximately normally distributed with mean of 120 and a standard deviation of 15. If the college requires an IQ of at least 95, how many of these students will be rejected? (about 45)
<7>If a certain machine makes eletrical resistors having a mean resistance of 40 ohms and a standard deviation of 3 ohms, what is the probability that a random sample of 36 of these resistors will have a mean resistance between 38 and 40.2 ohms? What is the probability that a random sample of 36 of these resistors will have a combined resistance of more than 1458 ohms? (0.6554; 0.1587)
<8> In a mathematics exam the average grade was 80 and the standard deviation was 6. All students with grades from 87 to 93 received a grade of B. If the grades are approximately normally distributed and 200 students took the exam, how many students received a B grade?(about 26)
<9> A normal distribution has mean=72 and unknown standard deviation. However, it is known that 30% of the area lies to the right of 80. Find the standard deviation. (15.4)
<10> State tax officials claim that the average amount of money claimed by all the taxpayers for charittable deductions during 1994 was $964 with a standard deviation of $102. Many samples of size 64 are taken. Find the mean of these samples and the standard error of the mean.(964;12.75)
<11>The average purchase by a customer in a book store is $4 with a standard deviation of $0.85. If 49 customers are selected at random, what is the prob that their average purchase will be less than $3.70? (0.0068)
<12>Verify that f(x)=x/8 can serve as the probability density of a continuous random
variable that can take on any value from 0 to 4. Find P(0
<13>The average amount of snow per season in Trafford is 44 inches. The standard deviation is 6 inches. Find the probability that next year Trafford will receive the following amount of snowfall. a) at most 50 inches of snow.(0.8413). b) between 38 and 42 inches of snow.(0.212)
<14> A manufacturer of ten-speed bicycles advertises that the time required to assemble its F4 model bike is normally distributed with a mean of 60 minutes. Furthermore, only 20% of the people will need more than 70 minutes to assemble the bike. Find the standard deviation.(11.9)
<15>On a recent physical endurance test, the score was found to be normally distributed with a mean of 112 and a standard deviation of 8. The judges have decided to award a trophy to the top 10% of the contestants. What is the minimum score that a contestant must obtain in order to receive a trophy?(122.24)
<16> The average height of all students in a college is known to be 65 inches with a standard deviation of 2.3 inches. If a sample of 36 students is selected at random, what is the probability that the average height of these 36 students will be between 64.8 and 65.5 inches?(0.6017)