93.06% of the race is longer than 236 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
Given that μ = 310, σ = 50
For x > 236:
From the normal distribution table:
P(x > 236) = P(z > -1.48) = 1 - P(z < -1.48) = 1 - 0.0694 = 0.9306 = 93.06%
93.06% of the race is longer than 236 minutes.
Find out more on z score at: brainly.com/question/25638875
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Explanation:
For company X, the equation is c = 10j + 115 where the 10j is the cost of buying all the jerseys (j of them). Then we tack on the flat fee of $115
The equation for company Y is c = 20j for similar reasoning as the previous company, but now each jersey costs $20. We don't add on anything else because there isn't an extra flat fee.
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We have this system
which are the equations for company X and company Y in that order.
Both equations have 'c' on the left side. So we can equate the right hand sides and solve for j
20j = 10j+115
20j-10j = 115
10j = 115
j = 115/10
j = 11.50
Recall that j is the number of jerseys. It's not possible to order half a jersey, so we have to round to the nearest whole number. The question is: which way? We're right at the midpoint between j = 11 and j = 12. Let's check both values of j to see what the costs are for each company.
Company Y is the cheaper option if you bought 11 jerseys. But we want to know when company X is the better deal. Let's try j = 12
This time company X is the winner in terms of the best deal (aka cheapest cost). If j gets any bigger, then company X is still the winner. So we can see that the minimum order must be 12 jerseys if we want company X to be the cheapest option.