While exercising, Carly burns 450 calories per hour biking and 620 calories per hour playing racquetball. Sarah burns 560 calori
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Answer:
Probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.
Step-by-step explanation:
We are given that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15.
A sample of 36 students was selected.
<em>Let </em><em> = sample average time spent studying</em>
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean hours spent studying = 25 hours
= standard deviation = 15 hours
n = sample of students = 36
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the average time spent studying for the sample was between 29 and 30 hours studying is given by = P(29 hours < < 30 hours)
P(29 hours < < 30 hours) = P(
< 30 hours) - P(
29 hours)
P( < 30 hours) = P(
<
) = P(Z < 2) = 0.97725
P(
29 hours) = P(
) = P(Z
1.60) = 0.94520
<em>So, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 and x = 1.60 in the z table which has an area of 0.97725 and 0.94520 respectively.</em>
Therefore, P(29 hours < < 30 hours) = 0.97725 - 0.94520 = 0.0321
Hence, the probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.
<h2>Hello!</h2>
The answer is:
They spent $176 together.
<h2>Why?</h2>We are given an expression which represents the money spent for each girl, it's a function of time and it will show how much they can spend in terms of hours.
Assuming that you have committed a mistake writing the equation, otherwise, the given options would not fit, the expression is:
Now, from the statement we know that the function represents how much money each girl spent, so, if we need to calculate how much money they will spend together, we need to multiply the expression by 2, so we have:
Then, calculating the spent money for 2 hours, we need to substitute the variable "x" with 2.
Calculating we have:
Hence, we have that they spent $176 together.
Have a nice day!