Answer:
a.
b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%
c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %
d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%
e. 86 should have a battery life of at least 9 hours
Step-by-step explanation:
From the given information;
Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :
where A and B are the two parameters of the uniform distribution
From the question;
Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours
So; Let A = 8,5 and B = 12
Therefore; the mathematical expression for the probability density function of battery life is :
b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:
F(x) = P(X ≤x)
F(10) = 0.4286
the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%
c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?
The battery life for an iPad Mini will be at least 11 hours is calculated as follows:
the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %
d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?
Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%
e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
The probability that battery life of at least 9 hours is calculated as:
NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:
n = 100(0.8571)
n = 85.71
n ≅ 86
Thus , 86 should have a battery life of at least 9 hours