can you please help me with these practice questions.

1. Suppose approximately 59% of all students study after midnight. For random sample ofn=3students, letXbe the number of students that study after midnight. Complete the following table for the binomial distribution ofX. Keep at least 4 decimal places.

X	P(X)
0
1
2
3

Determine the mean and standard deviation ofX

Keep at least 4 decimal places.

a)The expected value ofX=

b)The standard deviation ofX=____

2. Megabus Canada Company trips from Ottawa to Petervborough are on time 70 % of the time. Suppose 11 trips are randomly selected, and the number on-time trips is recorded. Round answers to 3 significant figures. a)The probability that exactly 9 trips are on time is = b)The probability that at most 8 trips are on time is = c)The probability that at least 9 trips are on time is =

3. A particular fruit's weights are normally distributed, with a mean of 723 grams and a standard deviation of 6 grams. If you pick one fruit at random, what is the probability that it will weigh between 716 grams and 720 grams ________.

3.A particular fruit's weights are normally distributed, with a mean of 355 grams and a standard deviation of 11 grams. The heaviest 4% of fruits weigh more than how many grams? Give your answer to the nearest gram.

4. Supposezis the standard normal variable. It is suggested that you draw the normal curve for each of the following probability statements to visualize the required area. Report answers accurate to at least 4 decimal places.

1. P(z-0.3)=
2. P(z-1.57)=
3. P(z<0)=
4. P(z<4.78)=
5. P(-2.16z<1.42)=

5.Supposezzis the standard normal variable. Draw the normal curve for each of the following probability statements to visualize the required area and determine the missing values. Report answers accurate to 2 decimal places.

1. P(z<)=0.1977)
2. P(z>)=0.4129)
3. P(z<)=0.5

6. A particular fruit's weights are normally distributed, with a mean of 253 grams and a standard deviation of 31 grams. If you pick one fruit at random, what is the probability that it will weigh between 232 grams and 260 grams _______.

7. A particular fruit's weights are normally distributed, with a mean of 652 grams and a standard deviation of 7 grams. The heaviest 15% of fruits weigh more than how many grams? Give your answer to the nearest gram.

8.Assume that the number of cases of COVID-19 per day are normally distributed with a mean of 462 and a standard deviation of 51 on any given day.

Enter your answers in decimal form rounded to 4 decimal places

(a) What is the probability that on that day there will at most 389 cases? (b) What is the probability that on that day there will be between 373 and 604 cases? (c) What is the probability that on that day there will be at least 498 cases?

9. Deandre and Kevin began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Deandre took a test in Science and earned a 72.1, and Kevin took a test in Social Studies and earned a 69.5. Use the fact that all the students' test grades in the Science class had a mean of 72.6 and a standard deviation of 10.1, and all the students' test grades in Social Studies had a mean of 62.1 and a standard deviation of 9.1 to answer the following questions. a)Calculate the z-score for Deandre's test grade. z= b)Calculate the z-score for Kevin's test grade. z= c)Which person did relatively better? a)deandre b)kevin c)they did equally well