Alice ran 2 miles in 12 minutes. Jonathan ran 5 miles in 40 minutes. If both were traveling at a constant speed, who was going faster?

Alice

Step-by-step explanation:

If Alice was running 2 miles in 12 minutes then in two hours she would have ran 20 miles. If Jonathan was running 5 miles in 40 minutes then in two hours he would've ran 15 miles. In conclusion Alice would go faster if she was traveling at a constant speed

Probability that the number of poppy seed bagels sold on a particular day exceeds 400 is 0.0475.

Step-by-step explanation:

We are given that the shop owner determined that the daily demand follows the normal probability model with mean 300 bagels and standard deviation 60.

Let X = daily demand of poppy seed bagels

The z-score probability distribution for normal distribution is given by;

           Z =  ~ N(0,1)

where, = mean bagels = 300

             = standard deviation = 60

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 number of poppy seed bagels sold on a particular day exceeds 400 is given by = P(X > 400)

 P(X > 400) = P( > ) = P(Z > 1.67) = 1 - P(Z 1.67)

                                                   = 1 - 0.95254 = 0.0475                       

So, in the z table the P(Z  x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.67 in the z table which has an area of 0.95254.

Hence, the probability that the number of poppy seed bagels sold on a particular day exceeds 400 is 0.0475.