Provide the logical reasoning for all questions.

1- You are told that X is a normally distributed random variable with = 0.83 and 97.5% of the values are below an X value of 22.

What is the value of ?

Please give your answer correctly rounded to two decimal places and with logical reasoning.

2- Say, Apple Inc. claims that 24% of all Apple device users own an iPad. If a random sample of 217 Apple device users is selected, what is the Z score if 40% of those sampled own an iPad?Assume the conditions are satisfied.

Give your answer correctly with logical reasoning and rounded to two decimal places.

3- Information on a packet of seeds claims that the germination rate is 0.96. Note, the germination rate is the proportion of seeds that will grow into plants. Say, of the 203 seeds in a packet, 131 germinated. What is the value of the number of successes in the population? Please give your answer correct to two decimal places.

4- You are told that the distribution of television weights is normal, with a mean, of 10.5 kilograms and a standard deviation, of 2.5 kilograms. If a random sample, n of 8 televisions is selected, what is the Z score for a sample mean weight,xof 14 kilograms?

5- The lifetime of a product (years) is exponentially distributed with = 0.03.

What is the probability that this product will last between 5 and 14 years?

6- A salesperson created a 99% confidence interval of (262.23, 602.45) megabytes per month to estimate the average capacity usage of an iPhone. What is the value of the width of this confidence interval? Please give your answer correctly rounded to two decimal places and do NOT include units in your answer.

7- An electricity provider wants to estimate the meantime it takes for customers to get an electrical fault resolved. The provider took a random sample of 36 customers who had recently reported an electrical fault and found a mean time of 9.42 hours. Assume the population standard deviation is 0.72 hours. What is the value of the margin of error for a 95% confidence interval?

Please give your answer correctly rounded to two decimal places and do NOT give units.

8- The production manager at a textile mill, believes that a new machine, producing cloth, is not working according to the company's specifications. The company requires that the cloth should have a mean breaking strength of 46 Kg. A sample of 62 pieces of cloth reveals a sample mean breaking strength of 39.8 Kg and a standard deviation of 0.8 Kg. If the manager wants to do a hypothesis test to her belief, what value of the mean would be used in the null and the alternative hypotheses?

9- The production manager at a textile mill, believes that a new machine, producing cloth, is not working according to the company's specifications. The company requires that the cloth should have a mean breaking strength of 46 Kg. A sample of 62 pieces of cloth reveals a sample mean breaking strength of 39.8 Kg and a standard deviation of 0.8 Kg. If the manager wants to do a hypothesis test to her belief, what value of the mean would be used in the null and the alternative hypotheses?