Statistics and Probability Answers

. The length of time X that the battery in Stella’s phone holds enough charge to operate is normally distributed with a mean μ = 25.6 hours and a standard deviation of σ = 0.32 hours. Stella forgot to charge her phone yesterday, and it’s been now 26 hours since the phone was charged. What’s the probability that the phone will operate?

Hint. The phone will operated if this particular time the battery lasted 26 or more hours

If the pattern below is continued, find the 8th fraction in this sequence:

1/2 , 2/3, 3/5 , 5/8;

a. 21/34

b. 12/36

c. 34/55

d. 13/21

A half ton truck carrying sand , to capacity breaks down. The owner sends quarter ton truck to load the sand and deliver it to the client. How would you calculate the number of quarter ton trucks needed to curry the sand?

a. 1/2 × 2

b. 1/4 + 1/2

C. 1/4 × 2/1

D. 1/2 + 1/4

The cost of renting a consulting room for 4 hours is R96.80. The costing of renting a room is proportional to the number of rental hours. Which of the following is not an equivalent rate to 4 hours for R96.80?

1. 6 hours for R145.80

2. 3 hours for R72.60

3. 7 hours for R169.40

4. 5 hours for R121.00

According to the Sleep Foundation, the average nights' sleep is 6.8 hours. Assume the standard deviation is 0.6 hours and that the probability distribution is normal.

1) What is the probability that a randomly selected person sleeps more than 8 hours?

2) What is the probability that a randomly selected person sleeps 6 hours or less?

3) What is the percentage of people sleeping between 6,2 and 7,4 hours ? 

4) Compute once again the above probabilities based on a standard normal distribtuion.

1. The mean, variance,  β₁ and β₂ of a distribution are 10, 15, 1 and 3. Find the four moments about origin.

1. Two teachers teach two groups of students who are studying the same subject. In the first group, 30 students were selected of which 11 failed the quarterly examination while in the second group, 10 out of 24 students failed. At x = 0.01, is it valid to conclude that the rate of failure in the first group is less than that of the second group? What is the implication of the results of this test

According to a factory employer, the mean working time of workers in the factory is 6 hours with a standard deviation of 0.5 hours. A researcher interviewed 50% of the employees and found out that their mean working time is 8 hours with a standard deviation of 1 hour. The a level is 0.05.

In symbols?

• Find each of the following percentile points under the normal curve.
• Complete your procedures.

1. P₉₉
2. P₉₀
3. P₆₈
4. P₄₀
5. P₃₂

Akali made a bet to Kai'Sa wherein in 7 throws, Seraphine will hit the bull's eye once, 3 triples, 3 doubles, and no misses.

Seraphine's stats are as follows,

0.09 for bull's eye, 0.22 for triples, 0.34 for doubles, and 0.03 for a complete miss.

What is the probability of Akali's prediction?

Answer (decimal form, 4 decimal places)