Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of
![](data:image/png;base64, /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAMCAgMCAgMDAwMEAwMEBQgFBQQEBQoHBwYIDAoMDAsKCwsNDhIQDQ4RDgsLEBYQERMUFRUVDA8XGBYUGBIUFRT/2wBDAQMEBAUEBQkFBQkUDQsNFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBT/wAARCAARAEsDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD9DdH8f69d/GjxL4Nu7LTo7Sw0K01e0eGSQyOZrm7hAkcgADbbI2AnylyMtgE1vA/iXx3b/E/VfCvix9B1ezGmR6ra6loNlNZm03TNGLe4jkmm3FtrFJVZA3lS/IuKig+GHjC1+N+u+O4/Fmh/2dqGjw6PFpLeH5jNCkLTyQu1x9tw5Etw5bES7lCqNhy5g+H3w7+JnhF7xtU8ceEtZkvJVnubuLwjc29zcSeYm5pHOpup/dB41VVVUJQgFU2NaUfdafTX8fy0enZLa5c7Pm5fK33K/wCq+d+iNXRviBrlz8afEng6+sbFLHT9CtNXtWtHd5pPOubuIK7NtX7tsrYC8FyNzAZPnn7P/wC0D4k+K3jBLG/uPD0sb6dJd6loNpaT2eqeGp1kVEt7nzpm+0hz5oEqRxDMWQCGGOzT4S+JpfjVr/jG68VaW+g6vo0Whto9vossV3FBE07xsLv7Wy799zISfJwVCgBSCxg8A/BHV/DviLw7qXiHxRZa/F4XsJdM0NLPRVsZkgdUQ/aZfNk81gsajEawpnJKEhSqVk00unW+7v8Alp39Ur3U2m2orTT8lf73f/Jm74j+PPgfwl4mj0LVdYktbxriKzkuRYXMllbTy48qGe7WMwQSPuQKksis29cA7hltp8evBd7p+l3sd9qC22o603h6FpdFvYyl+JDGYZVaEGH5xtDShVJxgnIrmPE/7PupeI9R8RacfFscfgPxHqUWq6poc2l+bdmZPKLRwXRlCxwyGBCyNC7fM+11yNudrP7Onie4kvoNL8dafY6UfFUXi2ytbnQGuJI7kXAnkimkF0nmxFgdoRYmXIyzgYOMXLmhzLR25vLWN7fLmt3stFs4ndRk479Pulb8eVW6a6vRnV2P7SfgC/1DTLJNR1OGXUdTfRYXutA1C3iS+Vtn2aWWSBUhlJxtWVlL5BXcCM6Vz8c/Bdnrl7pdxqk8D2STvPfS6ddLp6GHPnJ9tMf2cyJtbdGJC4wfl4rhl/Z/8WTeDdT0q78baPNqs3i+HxbZ30fh2VIYHS7S58iSH7aTICybdwkQgHoSOXaj+zhqmreAvF/w+vPFtpceA9aF3JaWsmih9QspZ5zcfNO0xinjWVmIR7cEr8rM3UkXJ005L3rfK9l+t112370/4jUfhvv5Xev/AIDZ99evTr0/aA8FyaRcX4udXDwXP2N9Lbw/qC6p5uwyALYGD7SwKKzhljIKqzA4BI7Lw14j0/xfoFhrWlTNcadfRLPBK8TxMyHoSjgMp9mAI9K8I0/9le70fwZZaTpqfC7StRt9QF+0+nfDgW1pKwiMayGCO+V0nGTiZJl4JXbg4r27wT4bk8H+FNM0abVL3W5rOERvqGozNLPO3UszMSTyeMk4GBk4zWndf1tr+P5fMhNvp/V/8jcooooKCiiigAooooAKKKKACiiigD//2Q==)
and a standard deviation of 0.04 ounce. Find the probability that the bottle contains fewer than
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of beer.
◦ 0.0062
◦ 0.5062
◦ 0.4938
◦ 0.9938