Can you help me with the following practice questions and solutions on Data Analytics in Normal Distribution?

1. Find the following probabilities:
3. a) P(Z < 2.34)
4. b) P(Z < -1.45)
5. c) P(Z > 2.34)
6. d) P( -1 < Z < 1)

4 points

1. Explain what the symbolZ0.05represents and state its value:
2. (choose one of the following answers..)
3. a.Z0.05represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value isZ0.05=1.65.b.Z0.05represents the z-score, the value of the standard normal distribution, at which the probability of being less than that value is 0.05. The value isZ0.05=1.65.
4. c.Z0.05represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value isZ0.05=2.58.d.Z0.05represents the z-score, the value of the standard normal distribution, at which the probability of being less than that value is 0.05. The value isZ0.05=2.58.

1. Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing process is such, however, that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights can be approximated by a normal distribution with mean 90 grams and a standard deviation of2 grams.
3. i) What is the z-score relating to the value 87g ?(1 dec place)
5. ii) Find the probability that a randomly selecteditem will weigh less than 87g.(4 dec places)
7. iii) What is the z-score relating to the value 95g ?(1 dec place)
9. iv) Find the probability that a randomly selecteditem will weigh less than 95g.(4 dec places)
11. v) Find the probability that a randomly selecteditem will weigh between 87gand95g.(4 dec places)
13. vi) If it is requested thatitems having a weight in the top 5% of weights of allitems are to be classified as defective, over what weight shoulditem be classified as defective?(1 dec place)

1. The distribution of actual weights of 8 oz. chocolate bars produced by a certain machine is normal, with a mean of 8 oz. and a standard deviation of1 oz.
3. i) Bars of weight less then 6 oz. are classified as small, and are not issued for retail. What is the z-score relating to the value 6 oz. ?(2 dec places).
5. ii) Find the probability that a randomly selected bar will be small.(4 dec places).
7. iii) If it is requested that bars having a weight in the top 10% of weights of all bars are to be classified as Large, over what weight should bars be classified as Large?(1 dec place).