# Normal Probability & Z-score

See attached file for questions 8 and 9.

1. The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

A- Sample of n = 75, the probability of a sample mean being greater than 229 if u = 228 and o=4.4 is (round to four decimal places)

B- The sample mean (would or would not) be considered unusual because it (does not lie, lies) within (1 standard deviation, 2 deviation, 3 deviation) of the mean of the sample means.

2. A drug tester claims that a drug cures a rare skin disease 73% of the time. The claim is checked by testing the drug on 100 patients. If at least 68 patients are cured, the claim will be accepted.

Find the probability that the claim will be rejected assuming that the manufactures claim is true. Use the normal distribution to approximate the binomial distribution when possible.

The probability is ___ (round to four decimal places)

3. A vending machine dispenses coffee into an eight ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.05 ounce. You can allow the cup to overfill 10% of the time. What amount should you set as the mean amount of coffee to be dispensed? = ____ (round to two decimal places)

4. Find the indicated area under the standard normal curve. The area to the left of z=-1.27 under the standard normal curve is ____ (round to four decimal places)

5. Find the normal distribution shown on #5 on the attachment) find the probability of z occur in the indicated region. The probability is =____ (round to four decimal places)

6. Find the indicated z-scores shown on #6 of the attachment. The z-scores are =____ (use a comma to separate answers as needed. Round to two decimal places as needed)

7. The average math SAT score is 516 with a standard deviation of 117. A particular high school claims that its students have unusually high math SAT scores. A random sample of 45 students from this school was selected, and the mean math SAT was 545. Is this high school justified in its claim? (Yes, no) because the z-score _____ is (unusual, not unusual) since it (does not lie, lies) within (1 standard deviation, 2 standard deviation, 3 standard deviation) of the mean of sample means.

8) See attachment

9) See attachment

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#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

Normal Probability and Z-score

Lab technicians at a major mdical lab can process an average of 400 blood samples a day with a standard deviation of 50 samples. The processing follows a normal distribution.

Convert 445 blood samples into a z-value (standard score).

What is the area under the normal curve between 400 and 482?

What is the area under the normal curve for ratings greater than 482?

Interpret the result. What does the standard score represent? What does the area under the normal curve mean?

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