# Probability and Descriptive Statistics

Questions should be solved on excel file using excel functions.

1) Probabilities.

A fair coin was tossed 3 times. Calculate the probabilities of the following 6 events.

1. Three heads were observed

2. Two heads were observes

3. One head were observed

4. At least two heads were observed

5. No more than two tails were observed

2) A variable Z is normally distributed with µ=54 and standard deviation=12.3. Find the following probabilities:

1. P(40 < Z < 55.7)

2. P(Z = 64.9)

3. P(Z > 54)

4. P(Z < 48.1)

5. P(Z >= 63.4)

6. P( Z <= 70)

7. P(Z < 38.2 OR Z > 57.3)

3) Using Excel's standard functions,

- calculate the mean, variance and standard deviation of the students' grades presented bellow.

- Also, use the descriptive statistics tool and calculate various statistical measures.

90 93 63 55 93 85 79 95 83 61 82 95 66 51 99 50 95 63 69 90 59 57 63 77 75 54 69 67 79 52

4. Application Problems.

1. The life of an electronic transistor is normally distributed with a mean of 500 hours and a standard deviation of 80 hours. Determine the probability that

a. A transistor will last for more than 400 hours?

b. A transistor will last for less than 350 hours?

c. A transistor will last exactly 501 hours?

2. The weight of bags of fertilizer is normally distributed with a mean of 50 pounds and standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh:

a. between 45 and 55 pounds?

b. At least 56 pounds?

c. At most 49 pound?

5) Studying for MATH course

The amount of time devoted to studying MATH each week by students who achieve grade A in the course is normally distributed with mean of 7.5 hours and standard deviation of 2.1 hours. Find the probability that an A student study time per week is

a) between 7 and 9 hours?

b) less than 5 hours?

c) exactly 6 hours?

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#### Solution Summary

The probability and descriptive statistics are examined.